Fact that it assumes / supposes rationality at all is a major flaw in the theory.
No, it's really not. It assumes that people pursue stuff they desire, that's about it. Please give me an example where you claim it doesn't work, and it'll be either so unusual that it can be safely ignored by the model, or the person will be acting rationally about possible irrational desires.
Hm, I think part of the problem is, at base, we do live in a world of theft and violence. The initiation of violence is a part of life and existence. For example, how does a libertarian handle such a basic idea as "spare the rod, spoil the child?". How is the child supposed to be disciplined? If I betray someone, does that count as aggression? Should not traitors be killed? What about the disobeying of commands?
So a couple of points here. First, there's usually a big honking exception for children, as they don't know what they are doing. Second, betrayal is generally considered aggression under fraud (they promised X then refused to do X).
As for commands, those can be disobeyed unless the person commanded has consented to the authority ahead of time, at which point forcing the person to obey commands isn't aggression, as you agreed to it.
You bend everyone to the collective will and the covenant of non-aggression (at least among those in covenant) and violently punish people who breach that covenant.
What collective will? Following the NAP personally doesn't require a collective. Also, it doesn't require violence. It just
allows violence in response to violations, not demands it.
Which makes the NAP not really particularly useful as a fundamental moral access, because I'm not sure it really says much more than to follow the existing moral framework and at least don't break the rules.
Again, that's wrong. The NAP provides the framework by (somewhat ambiguously, admittedly) defining aggression.
Thus the somewhat utopian thinking that sometimes seems to come out of it, and the similar disconnect between reality one can feel between Libertarianism and the real world. I would agree the Libertarians may be less disconnected than the communist is, but on the other hand the Communist idea seems to have more power in practice: the ideas of Communism have been able to wield the power to conquer half the world, if not more, while Libertarianism gets 1% of support in America, which is the most pro freedom pro individuality place on earth as far as I can tell.
But the ideas of libertarianism are very influential in the United States, despite not being incredibly popular in whole. Free Speech, freedom of religion, freedom of association, free market capitalism, I could go on. Communism is successful at the point of a gun. Libertarianism is successful because people like the ideas it generates and implement them.
Even to take the libertarian/liberal as synonyms of each other, the Liberal ideal lost some time around the 1900s. Every Liberal party was close to a de-facto socialist party by that point it seems.
Liberalism seems often so impotent a force in the world.
Just to point out, the Republican party for a long time was the liberal party (probably until Trump), so I don't know what you are talking about. It basically inacted a ton of libertarian aligned agendas.