I appreciate how you're wrestling with these issues. Indeed, my political writings are mostly on liberalism and conservatism (link below).

And I'm pretty cynical about politics too, so I agree that sophistry is prevalent in that arena. But what you're leaving out here is philosophy. Rand was supposed to be some kind of philosopher or at least a thinker, not a politician. The ancient Greek Sophists thought that philosophy was all about rhetoric and underhanded tricks of persuasion, whereas Socrates, Plato, and Aristotle thought there were higher, epistemic and moral obligations, so philosophers should be above such tricks.

I'm more cynical about politics than I am about philosophy, which is why I frown on Rand's weak arguments. As I say in the article, it's understandable because she didn't train as a philosopher. She was literally an entertainer, as in she wrote screenplays and novels. She did have a personal philosophy, but whether that philosophy rests on solid arguments is the question at issue for me.

https://benjamincain8.medium.com/list/political-travesties-8b03df43308d