You can take anything too far of course, in particular when you try to take your political/economic ideas and make a personal philosophy out of them. Then you are in the realm of gurus, however rational they claim to be. You might as well critique religions on matters of internal logic. Its a pointless exercise.
Libertarianism, in general, is based on the idea of individual liberty as the primary political good, and on empirical observation of politico-economic "best practices". Rand did push on both these fronts, as did Hayek et. al. Rands heroes and heroines got things done, and their enemies were correspondingly incompetent.
I am sure Rand and Hayek and everyone else writing on libertarian theory would have a nice argument on WHY personal liberty is the primary political good - but thats where you have your disagreement with Rand.
You would get in the same trouble if you asked communists to answer WHY the working class deserved to rule.
Tell that to St. Thomas Aquinas.
Ayn Rand was no St. Thomas