I think the word 'anarchism' is actually synonymous with socialist anarchy.

As for the question itself I'm not sure the title question is connected to the folow up questions in the text.

For instance I don't know of many AnCaps here who believe that we wouldn't have the same human problems without a government, just that we don't need a monopoly of force in order to be able to resolve and deal with those problems.

As for your follow up questions:

Once in anarchy, what keeps a state from forming?

Depends on what sized area, I presume you mean the kind of state you have in america now where all your 50+ states are under one federal government? If so, the number one thing preventing it would be that unless you had a near unanimous consensus it would be near impossible to do so.

If someone wanted to take it over by force they would be coming up against not only a multiplicity of police-type services, defence companies, but also armed citizen militias, etc.

Even if one company managed to grow large enough to overcome that hurdle, if they started to violently impose a state-like structure on people, well they would need to enforce people to pay them. If there's no centralised tax structure in place, that means that either they would have to go door-to-door at local levels first to ensure compliance, before expanding that influence over people gradually by which time they would have to deal with 2 main issues -

1) the people they haven't forced into a tax structure stoping paying them, which means an immediate drying up of incoming funds. There's only so long you can keep paying and arming your soldiers without money coming in.

2) They would have to deal with violent resistance which means their own people been subdued/captured/killed.

Basically as Stefan Molyneax puts it, invading an established state is like capturing a cage of chickens, invading a stateless (but well defended) area that has no centralised control or source of funds is like running a a bunch of seagulls on the beach and trying to capture all of them.

Failing all of that, even if they did manage to form a government because it's just what the majority of people have decided, well yeah it's possible it could happen. But the possibility of having cancer return does not mean you shouldn't try to get rid of cancer.

The answer to your original question however is, no it's not meant to be utopian. Things would probably improve without a government but I don't think anyone here is expecting or has ever suggested that human problems would disappear. Humans aren't perfecting, no society will ever be perfect.