No.
Capitalism - the private ownership of the means of production - does not rely on any of those assumptions.
Certain schools of economics have posited that the optimum allocation of resources depends on perfect this, perfect that, and perfect the other.
It should be obvious that a theory resting on assumptions of human perfection is useless in the real world. But this is no more a criticism of private property, than it is of any other form of production. It simply fails to come to terms with the real issues. You are correct in pointing that out. You are not correct in thinking that demonstrates and concludes the case against capitalism.
The defence of capitalism does not rely on perfect anything. It relies on the fact that *consensual transactions are ethically and pragmatically better* than violence-based transactions and central planning, which is the only alternative for a civilisation, apart from mass starvation.
The fact that resources are scarce, and that this causes very real problems for man and society, is not caused by "capitalism" or "ideology", it's caused by nature. Capitalism more than anything in the history of the world has relieved these problems, especially for the poorest.
Just because nature imposes scarcity of resources on human action, it is not legitimate to assume therefore that a legal monopoly of aggression and threats - government - can magically make this problem better at no cost, or at optimal cost. It's nonsense - it has no basis in reality or reason. It is no better than a superstition, which is why all attempts at full socialism degenerated in short order into mass starvation.
"Or the fact that individuals make rational choices."
"Rational choice" doesn't mean a choice that you agree with.
All choices are rational in the sense that the person taking action believes there is some *reason* why his action will *cause* an *effect* that he finds more satisfactory; otherwise he wouldn't take any action. For example, even someone trying to improve crop fertility by doing a rain dance, is acting rationally in this sense: he believes the dance will improve fertility. It is not necessary for the belief to be true for us to understand that the action still has its logical economic consequences, for example, the costs of the dance. In this limited sense, all choice is rational, and that limited sense is all that is needed to explain the logical consequences of human action. Human action is *purposive*. This is axiomatic. It is the basis of understanding human action in general, and economic activity in particular.
But in the sense in which you mean "rational", i.e. the action *really does* logically tend to the desired end, then socialism would only be rational if people desired greater poverty, sickness and death. It is in no way an argument against capitalism.
"Such a system is not stable. Inevitably it WILL be destroyed. It's simply a matter of WHEN, not IF."
a) everything in the universe is not stable, is not sustainable. So what? The purpose of human action is not to reach some kind of abstract theoretical perfect stasis. The purpose of human action is to satisfy whatever want the people taking action, are trying to satisfy, by taking that action! It's you who are thinking purely theoretically.
b) even if we conceded that it's a problem that capitalism is not "stable" - (nothing is) - it doesn't mean that any alternative - ESPECIALLY government - would be any more stable. On the contrary, government MUST (not may) waste more resources to achieve the same result in terms of human welfare, so it's less stable, not more.
"Why do supporters of free-market capitalism think purely in theoretical sense, failing to take into account the many variables?"
I must beg you to permit to inform you that everything you are saying is mistaken. You have formed an opinion on the basis of theories that are mistaken - perfect competitition etc.
You've got it back the front. It's the opponents of capitalism who think in slogans and abstractions and aggregates, without ever coming to grips with the real issues.
In a nutshell, all critics of capitalism simply ignore the costs of all the alternatives they propose. But obviously if we ignore the costs, anything will seem beneficial! That's why socialism and government keeps *seeming* attractive, and keeps ending in waste, corruption and war.
If you want to know why everything you have said is illogal and mistaken, read "Human Action" by Ludwig von Mises - available free online.
If you don't, the less you exhibit your ignorance the better eh?