Well, you are partly on the way to working out the system I am building, called "Unification". You have correctly identified ownership as a major cause of wealth and income inequality in capitalism, but a full reformation of free markets must go beyond abolishing ownership, and address the other glaring defect: capitalism has one virtue, which is freedom. That is, you are free to do anything that isn't forbidden, whether it actually helps society or not. The theory is that enlightened self-interest will naturally cause people to punish bad actors and reward good actors. Of course, that theory depends on humans being rational actors, and we have far too many examples demonstrating otherwise.
So the defining principle of Unification is goodness, as in "make people good" rather than "make people free." There are many currencies in this system, but the discretionary currency, which I call Social Credit, is designed to be an explicit measure of the value which one contributes to society, rather than just yourself (capitalism assumes that helping yourself will ultimately help society, but fails for zero-sum games).
In capitalism, money creates money. That's why poor people work and rich people relax. The only difference between a poor black dude sitting at home collecting welfare checks and smoking blunts and a rich white dude sitting at home collecting dividend checks and snorting coke is that one was born poor and the other was born rich. Capitalism is completely ambivalent about these outcomes, in general. So to prevent people from mooching off inherited wealth, you need to eliminate wealth that produces wealth. You need to eliminate ownership. I replace it with something called Stewardship. Strict ownership is only possessed by the Unity, which is all of society together. Whenever someone creates an artifact, they consume resources owned by the Unity, and pay a use fee for as long as the artifact exists. However, they also become the Ultimate Steward of the artifact, and are legally responsible for its entire lifetime. When it is no longer usable, they are responsible for deconstructing it and returning its raw materials to the Unity.
Obviously, consumable items are consumable, and are the only artifacts for which stewardship can be fully passed to the consumer.
So, contrary to your idea, Unification doesn't eliminate rent, it rents everything. This has nice effects, however. If we think about products today, many of them are built with planned obsolescence, whether manufacturers admit to it or not. If you want a society that saves energy and resources, then you need to incentivize manufacturers to make artifacts as durable as possible. Capitalism doesn't reward creating products that last, because once a sale is complete, the capitalist no longer has a connection to the artifact (modulo returns, etc.). Under unification, the manufacturer does not get their entire investment back at sale time, because there is no sale time. Rather, they get a recurring return via the use fee ("rent"), which now incentivizes them to make products last as long as possible, especially since they must also pay for deconstruction at end of life. The construction and deconstruction costs are mostly fixed, but they can increase their profits almost without bound by improving durability/lifetime. Of course, more durable products are also good for consumers.
Furthermore, the accelerating rate of change means that you can't create a product today and expect it to be current in 20 years without changes. So manufacturers are also incentivized to make products modular and upgradable.
There's a movie trilogy called Zeitgeist which is full of conspiracy theories and some other nutty ideas. But it has the honorable goal of presenting a society which is "post-scarcity". They focus excessively on money, even though money, per se, isn't the root evil. They try to make everything free, declare that people no longer have to work, and that AI will save us all by allocating resources fairly and intelligently. Needless to say, I think this is hopelessly optimistic. Not only do I think humans want to work, this model tells us nothing about how to get from here to there.
But "post-scarcity" is a valuable concept. Unification recognizes that some goods are "exclusive" (like an ice cream cone), while others are "non-exclusive" (like a digital song track). To that end, consumers only pay for exclusive access. That is, money is only used to de-conflict competing access claims for artifacts that can only be used by one person at a time (like clothes). So how do artists get compensated? Well first, let's talk about basic needs.
Medicare For All
Society today has reached a point where people are beginning to consider truly universal health care. But in a society of the future, where the goal is to make everyone as productive and happy and healthy as possible, this is simply a non-negotiable requirement. Under Unification, not only is health care free, so is education, housing, food, transportation, communication, power, water, and everything else a person needs to survive and thrive. That being said, there are still tiers and markets. The defining concept here is "Baseline". This is similar to Universal Basic Income, except much less free and much more precise. What Baseline provides is a solid 3000 calories per day, with the full complement of micro-nutrients. All food has a dual-price structure, where some portion is priced in BreadCoin, which is the baseline currency for food, and the rest is priced in SocialCredit. The BreadCoin portion is derived entirely from the nutritional content of the food (macro+micro nutrients), with healthy food having high value and junk food having low value. Thus, a raw peach might have a price of 200 BC + 0 SC, reflecting the fact that it is highly nutritious and has no value-add beyond growing and harvesting it. Whereas, a bag of chips may have a price of 20 BC + 500 SC, reflecting the fact that it's mostly empty calories with a bad micronutrient balance, combined with the fact that it's designed to be addictive. So, this causes healthy food to be cheap, and junk food to be expensive. You still have markets, free food, and luxury food, but you skew the incentives towards positive outcomes.
Now, the BreadCoin is not funded via taxes. There are no taxes in Unification. Instead, BreadCoin is created on demand. Yes, you just make up money ex nihilo. This sounds insane, until you consider that this is also how private bank loans are created under capitalism. No, really. Look it up. In particular, look up the difference between M0 and M1, and think hard about what "broad money" is. Now, when the BreadCoin is paid to the grocer, it gets converted into SocialCredit, because the grocer/farmer have done a social good. So we feed everyone by printing money. Oh noes!!! Runaway inflation, right? Well, no.
As you can probably guess, we pay for all Baseline services in the same way: we print money like madmen. And the provider receives compensation as SocialCredit. So how do we prevent inflation? Well, one of the other glaring holes in capitalism is that it's not a closed system. Anything without a price is an "externality", like clean air, clean water, biodiversity, quiet. Unification, on the other hand, is a closed system. Every resource has a price. Furthermore, land is very expensive (and owned by the Unity, of course). So land rents alone can act as a money sink. But power and raw materials are also "owned" by the Unity, and so those will also soak up excess currency.
Now, when we say that "biodiversity has a price", what the heck do we mean? Well, today, only 10% of land animals are "wild". The rest are domestic, meaning "food animals." Yeah. We killed the majority of wild animals so we could eat burgers and ham. That's not even talking about fish. And the problem is that wild animals are not economic agents nor priced assets within capitalism. Under unification, they are that and more: they are full members of the economy. So when we ask the question: "How much habitat should wild animals get?" we are at a loss for a principled answer. The unification answer is: "All species should be allowed to achieve their natural carrying capacity". So if deer can survive at 30 individuals per km^2, and humans could survive at subsistence at 3 individuals per km^2, then that is the "natural carrying capacity" for those species (which, of course, varies by biome).
Obviously, some species are over-populated, while many are under-populated (threatened, nearly extinct, etc.). Instead of land being traded only by humans, land is traded by all living things, with corporations acting on behalf of non-human species. Each species is represented by some corporation (with many corps representing large taxa of related species). And each corp receives a "land entitlement" inversely proportional to their population load, which is current population / carrying capacity. So if deer are over-hunted and only at 50% capacity, then they get 200% of the default land entitlement due to reduced numbers. Endangered species get massive entitlements. Humans get a pittance.
Naturally, this forces humans to give up huge tracts of land, mostly farms, and concentrate in cities. This also forces us to grow nearly all food indoors, in massive urban greenhouses stacked 20 stories high. On the other hand, wild species would rebound significantly with the retreat of human development. And now you see why land is so expensive.
But how do we guarantee full employment, which capitalism cares nothing about? What about "the useless class", as some Silicon Valley venture capitalists like to say? Well, with long-duration goods, we can no longer rely on manufacturing to save us. But we still need to put people to productive work. The only thing of last value that we can produce with excess capacity is knowledge. And thus, we drive the economy from the top by creating demand for knowledge until we get full employment. That is, we generate research grants and employ Ph.Ds and incent folks to increase their education until every last economic niche is filled. And yes, we pay for those grants by printing money ex nihilo. Fun!
Ok, so we are creating knowledge willy-nilly, but we are also giving it away for free!!! How the heck do we stimulate economic activity if all music and media is free? Well, we compensate knowledge creators by paying them any time their knowledge is accessed. So musicians get 1 SocialCredit for every minute their song is streamed to a consumer. Yeah, that adds up fast. Researchers get 1 credit for every minute that someone reads their paper. A product reviewer gets 1 credit for every minute that a shopper reads their review. And where do these credits come from? We print them on demand!!!
But what about derived knowledge? A research paper is built on the results of dozens of other papers. For that, we build a massive Attribution Graph. This is a global distributed database (blockchain) which links all knowledge by reference/bibliography. When a paper cites 10 other papers, those citations generation "downstream attribution credits". So the primary author gets, say, 60% of the total revenue, and the remaining 40% is divided among the references in the paper. All knowledge must attribute contributing sources, and thus, credits will flow throughout the entire knowledge graph. Writing one widely cited paper can throw off massive credits for the rest of your life. And thus, researchers don't even need to be paid a salary. They can be expected to earn all their income from research credits!
As you note, share ownership under capitalism is highly inequitable. Capitalists are allowed to gamble with other people's labor. Under unification, every shareholder is an employee and every employee is a shareholder. Furthermore, wage slaves exist under capitalism, because it lets poor people trade away all risk in return for fixed income. This is necessary if you are poor because being poor reduces or eliminates your risk tolerance. With baseline, everyone has the same risk tolerance. Some people live better than others, because they spend their SocialCreds for above-baseline housing, food, clothes, etc. But nobody goes "bankrupt", even medically. At worst, you lose all your credits, and have to live at baseline. You still get total medical care and all the education you need to start your next venture.
Unification forbids wages. All income is generated as shares of profit. All "partners" share in revenue risk, and so they are all invested in the corporation. To prevent capitalist shareholders joining several corporations but only actually working at one of them, there is an additional provision that you only earn profits from hours worked and logged. So in this respect, everyone is also an hourly worker. If someone who fancies themselves a CEO wants to join 10 corps, they are free to do so. But they will only earn the income of one corp, because they can't work 40 hours a week at 10 jobs. Also, few corporations would be willing to hire someone who can't put in a reasonable number of hours.
Unification also has dozens of other systems in place to repair the defects of capitalism. Is it capitalist? No. Yes. Is it communist? No. Yes. Is it socialist? No. Yes. I mean, there is no private ownership, but it's driven by markets, and "the state" provides for every citizen. So it's kinda "all of the above". I didn't even get into the legal or political system, but one could even make a case for anarchy being a component. Anyway, if you want to know more, I can explain it, but this answer is already way too long. ;)