Maybe idiot was too strong a word, but it was shorter than the alternatives. If she'd left it as a work of fantasy, and not encouraged adoption, I'd be less inclined to be disrespectful. However, she gave many talks on the subject and pushed her views as serious political philosophy. This was adopted by others and has pretty much ruined the whole party and platform.
So, maybe she isn't an idiot but is actually a genius for undermining a once viable political platform and duping young people into believing in fairy tales.
TL;DR: The "opposite" of a bad world isn't necessarily a good world.
It really is a broad spectrum and it's quite possible to have both authoritarian ideals in one category while having libertarian values in a different category.
I do favor the simplicity of the political compass with four points. It has a specific name but I can't think of it at the moment. It is simplistic, and reductionist, but it is handy enough for a forum post and adequate for generalized conversations.
But, as you suggest, it's much more complicated than that. We humans really do like putting things into boxes, or so it seems.
Libertarianism was never viable. It goes against human nature, just in the opposite direction from communism. Communism postulates that lazy people deserve everything (“to each according to his need”), so the wealthy and aspiring hate it. Libertarianism postulates they deserve nothing (“taxation is theft”) so the poor hate it. The gray reality is somewhere in between. The underlying truth of the situation is that when the poor have nothing to eat, they eat the rich, and moral absolutes do not help either side.
Libertarian is the opposite of authoritarian. Again, it's a broad spectrum on the political compass. There is still left and right. There are extremes and moderates. You're claiming absolutes and being polarized by assuming the loudest speak for every one.
If you read my posts, you'd see that I think Ayn Rand was a moron. You'd also already know that it is far more than just Randians. There's a wonderful Wikipedia article on the subject, if you don't believe me.
i just wanted to add that the poor don't eat the rich when they have nothing to eat. they do it much sooner, when they notice that the rich eat better and better and the quality of their food increases way quicker than theirs. that's when the biggest revolutions happen, anyway.
(guess what - i actually live in a post-communist country, too. most people here probably have no idea what they're talking about when they say communism.)