Once you get past the ideological answers, there are some very good reasons why communism will not only be a realistic but also attractive alternative to capitalism for the majority of society in the near to mid term future.
1. Politics abhors a vacuum.
There will always be competing political ideologies. Since the collapse of soviet communism, we've seen the rise of radical neo-Islam, in the form of jihadism, as a the chief political opponent to capitalism and the homogenising forces of globalised consumerism.
As economics professor Benjamin Barber argues in his 1995 clasic Jihad vs McWorld, unregulated market forces inevitably run roughshod over society's basic needs for justice and equitable access to resources. This conflict gives rise to reactionary movements such as jihadism. However, jihadism as a movement is fundamentally unpopular, even with the majority of the world's muslims, let alone the rest of the world, so the current competing ideology simply isn't palatable to most people.
2. Capitalism is fundamentally inefficient
The contemporary economic orthodoxy is that market forces are magically efficient at delivering goods and services. This is a refrain we hear quite often, usually alongside the inefficient state spending fallacy.
In reality, market forces are grossly inefficient at delivering goods and services where they are needed. According to the World Bank (hardly a revolutionary organisation), twenty million children starve to death each year. Not because there isn't enough food to go around, but because they lack the economic resources (i.e. money) to buy it. Meanwhile, vast resources are diverted into the production of superfluous goods and services such as electronic gadgets, war materials and propaganda.
This is only one example. There are two billion people currently living on less than two dollars a day, all of whom struggle with the basic necessities of survival, let alone justice and economic equity. Even in wealthy nations such as the United States, the middle and lower classes are becoming poorer as wealth is focused at the top, with many households increasingly unable to meet their basic expenses.
This is not because there are not enough resources to go around, nor is it a problem of logistics, or because people are greedy or stupid as the sleazier elements of the establishment would suggest. This is a purely economic problem because of capitalism's natural tendancy to focus wealth to the top. Capitalism redirects resources from things people actually need, like food, medicine, clothing, shelter, etc., towards producing items and services which generate vast wealth for the power elite at the top of the system.
TL;DR Capitalism is fundamentally incapable of meeting the basic needs of society and grossly inefficient at allocating the supply resources.
3. The fallacy of choice
Capitalism creates a powerful illusion usually referred to as "choice". Basically, the idea that as a consumer in a market economy, you have the choice to consume or not consume, or to change your consumption as an intelligent economic actor. This is one of the core arguments of the conservative orthodoxy, that capitalism is wonderful because it delivers all this choice.
However, that choice is of little value if you cannot afford the options on offer. It will matter very little to you if a choice of medical care is available to you, if you can only afford substandard care, or no care at all.
Likewise, it also matters little if the choice is between very similar items, making your "choice" even more illusory. Voting once every five years, where your choice is between a right-wing party, and an even more right-wing party. Or sending your children to a school which cannot afford to teach science or one which teaches faery stories in place of science.
The choice offered by capitalism is largely illusory or unattainable for the majority.
4. Indefinite growth is unsustainable
Capitalism is predicated on the concept of unlimited growth. However, we live on a planet with finite resources and a limited capacity to store and transform industrial waste. Most people recognise that we need to reduce our consumption, to save something for tomorrow, however the capitalist economic system requires ever increasing production and consumption to generate profits.
A serious reduction in human population or consumption would be an economic catastrophe in the context of the current economic system. Capitalism is fundamentally living in a state of denial which requires it to deny basic realities such as the widespread ecological problems of global warming, pollution and resource scarcity while promoting ever increasing consumption when we can least afford it.
5. Capitalism is undemocractic
While market economies in the industrialised world decline, corporate and ideological lobbying of politicians in the United States alone amounts to over $15 billion in the past five years. The aim of this lobbying is generally predictable: deregulation of industry, regulation of society. Companies are more free to pollute, exploit you at work, waste resources, hoard wealth, privatise public goods, and other social ills, which civil society is less free to do anything meaningful to fulfill its need for social justice.
Democracy is increasingly an illusion, reduced to another form of market "choice" between nearly identical products, rather than a true form of representative government. It is a democracy, it's just that it's one dollar, one vote, and big business has a lot more dollars than you.
6. Most work done in capitalist societies is useless
Back in the 1950s, futurists were fond of predicting that by the twenty-first century we'd all be working fifteen hours weeks or less because of all the automation we'd have by now. The reality is that we're all working fourty hours a week or more. So what happened to all the automation?
In fact it's already here, so why are we all working so much? The truth is that most jobs in a capitalist economy are actually useless with respect to meeting the needs of society. Think about how many people work in marketing, sales, public relations, information technology, lobbying, accounting, advertising, commercial law, patent and intellectual property law, policing crime related to poverty, design of the many unnecessary consumer products, transporting all those products, and so on.
On top of that, add the number of people who work in the massive service sector, providing us with services such as cooked meals, laundry services, entertainment, and so on, all because we're too busy working to do these things ourselves.
Now compare that massive army to the number of people who actually do useful jobs, such as growing food, making medicine, undertaking research, nursing the sick and elderly, and so on. I'm not saying that all luxuries should be abolished, but most of the work being done in market economies does not benefit those societies. So why is it being done? Because it meets the needs and agenda of the those at the top of the capitalist economic system. It's no surprise that corporate lawyers make six figures, while people who actually do useful work are mostly grossly underpaid.
7. Top heavy economies become unproductive and fail
A long-term view of history shows us that many previous civilisations such as the Roman Empire, the Mayans, the classical Egyptian empire, the Khmer Empire, the Soviet Union and many others followed a predictable path: power and wealth is increasingly concentrated at the top until that society is unable to meet the basic needs of its middle class. Eventually it becomes so top heavy, corrupt and ideological that it becomes unable to solve the political, economic or military problems that are part of its environment. At that point, the civilisation is doomed. It may stutter on for a while, but the overall trajectory is downward.
In the past, this wasn't such a problem, because when one civilisation failed, there was always another one starting up in the next kingdom along. However, today we live in a single, globalised market economy, and when it fails there will be nowhere else to go.
Many of the indicators for collapse are already in place. The middle classes in the United States are disappearing, with many professionals unable to find steady employment or meet their basic financial needs without going into debt. Society is dividing into the privileged few and an impoverished working class. For the first time in living memory, the next generation will have a lower standard of living than the current generation. Resources are rapidly depleting and environmental collapse is likely to happen within a hundred years. Ideology is rapidly replacing science and rational debate, with the conservative agenda increasingly dominating public discourse and education.
In short, the global capitalist system is beginning to implode under its own weight, and those at the top know that the peasants are coming for them with their pitchforks. This is why we're seeing the increased militarisation of civil police forces and the use of violence and legal intimidation as a first recourse.
In a post-scarcity society fatigued by widespread poverty, the excesses of the super-wealthy elite, and the basic inefficiencies and injustice of capitalism, a new economic and social model based on the just distribution of resources will seem very attractive. At the same time, you'll have a population angry and desperate for change: ripe conditions for revolution.
The use of computers to solve economic problems is certainly realistic as these are well understood, well defined and structured problems, the ideal kinds of problems for existing computer technology to solve. Those I really see this as social economists working with spreadsheets, resource planning and logistics applications, much as large corporations and governments already do today, but with social benefit rather than surplus value (profit) as the goal.
As an additional benefit, a command economy is free to deliver whatever is actually needed and wanted by society within the limits of available resources, without the distortions imposed by the capitalist need for profit. So from the point of view of consumers, assuming that the government remains democratic and responsive to civil society, it will be more efficient at delivering what people want and deliver real choice (because the goods and services on offer will be broadly attainable).