The problem with anarchy is the non-neutrality law and order, which is necessary to maintain individual rights. How would you stop the next guy from killing you without some maintenance of law and order? Ancaps say privatize everything, but does opening the use of force to profit really sound like a good idea? Wouldn't that lead to the creation of a permanently violent society? Again, ancaps say no, because violence is expensive for all parties - which I don't agree with. Violence is only expensive for who it is directed against, not those profiting. I'm not gonna get into detail about this, I just don't imagine anarchism working well for the individual (though it might sound promising on paper).
As far as the state goes, I agree that it is coercive, simply because it requires taxation to exist. I don't have an easy solution to this problem either, there are speculations about how we could fund a state without taxation, one of those being voluntary means of funding government, but I fear that would short-circuit the neutrality of government. The reason government is necessary is because otherwise individual rights cannot be effectively protected. So, a collective entity exists to protect the individual.
Corporations, too, should respect law in my system. They are not above it. And since the role of government is to protect individuals from violence/coercion, that includes from corporations who would break the law. Easier said than done of course, that much is true, but I think it can work.