You've described what the AI (ASI) can do - but what about the rest of its makeup?
Does it have a moral code?
Are there things it won't do, even if convenient and helpful to its mission - lie, manipulate, kill, alter DNA, rewrite history, cull rebels, create or encourage conflict? Do ends justify means, or does it even have a concept of morality beyond the fact that humans have some odd superstitious/irrational/evolutionary-artifact beliefs about "ethics"?
What are its goals, motivations - what outcomes does it want?
The devil is in the details - what does it really want? Human happiness, satisfaction, long-life, colonization of the stars, a healthy planet, for human civilization (or just life on Earth) to be sustainable and near-eternal?
Does human suffering concern the AI? Loneliness? Lust? War? Crime? How about the pleasurable feeling humans get when they think themselves superior, responsible for things, in control? Sadists are people, too (people who experience pleasure from others receiving pain) - does the AI concern themselves with what they want too?
How does it measure success?
Does it use some form of perfect polling, and success is a matter of opinion? What about when people express negative opinions about, say, improving the lives of people that are hated or discriminated against? And what about the fact that people often say one thing and do another — like say that don't like how much violence is portrayed in mass media, yet consume it with reckless abandon?
Humans have some very odd biases and their opinions are highly manipulable, but they are also varied and value things differently. One person might want the environment to be left untouched by civilization, while another wants to enjoy low-impact experience of it (hiking, camping), while another would be fine if you sliced a bunch of it up and put in smoother highways and some better parking.
How does the AI determine what outcomes are better or worse, when humans themselves disagree with each other?
What is its sense of time?
How does the AI view time, since it is presumably effectively eternal? Is it in a rush, considering a kind of human-suffering-per-minute metric where it wants to make things better ASAP, or does it say "how can I make the optimal environment for humans 100 years from now"?
If the AI calculates that humanity as a whole would be better off if there were less humans to take care of, would it let the currently living die of natural causes? Reduce the birthrate (through medical or cultural persuasion)? Cut off a section of humanity and allow it to starve, or even just wipe it out of existence.
Ignorance is bliss, the AI must surely know, so as long as it prevents people from realizing what it is doing (or has done), then would that be fine with it?
What if it calculates that the ideal humanity is in fact retrograde — peaceable utopic bands of no more than 50 people, living in harmony with a highly hospitable (carefully engineered to be plentiful) environment? If someone has to be victimized occasionally, it can design 'fake' members of the tribe to ostracize — which weren't real people with feelings at all, so no harm done.
If that's what it decides, would it seek to bring about this end swiftly, or just sit back and let (or even actively encourage) humanity to destroy civilization so it can rebuild things better?
Or it could just biologically engineer humans to not be so darn difficult in the first place! Homo Sapiens Familiarus... the happier humans.
Who's a good boy?
Humans Have Limited Needs, Infinite Wants
The nature of humans is that satisfaction is satiation - the feeling is temporary. Some humans work to be content and satisfied with life as it is, while some are never satisfied for long. It's always something - if you have a car, you need a better one, and our economic systems ensure there is always a better car.
The trick is, there's two ways to improve this state: get more, or want less. The AI could freely choose both, depending on the answers to the above questions.
Way Beyond Post-Scarcity
If you just want to know what life would be like with a God That Gives Us Awesome Free Stuff All The Time, Woohoo™, you're just looking for a "post-scarcity society".
But if you want to detail what would happen with a super-powerful intelligent entity that would try to make humanity better off, you've got a lot of questions to answer about this might-as-well-be-a-god entity! Ultimately, this is a complete wild-card, and you can take the story - and make the ending - pretty much anything you want.
If the result isn't a society that is probably great but is still somehow unsettling or disturbing to many people, or with a questionable/arguable process that brings it about...then I'd say you were, in fact, doing it wrong!