As you must be aware, many smart people disagree with you about Rand, and can back it up with something better than a youtube video. And anyway, you said her philosophy contains certain flaws. That doesn't imply it's not valuable and useful overall, so even if I concede your points, it's not very important. The reasons I like Rand have nothing to do with "axiom of reflexivity of identity" or that other stuff you said.
edit: no online sources? I don't normally pay $35+ because a hostile, anonymous internet commenter said something would refute someone I respect but didn't want to explain the ideas himself.
As for $35, it pains me to mention libraries...it was a source, with a link so that you could see something about the book.
I can't say I know of a single public intellectual or professional philosopher who takes Rand seriously. I do know of a well-regarded mathematical logician who does, but this is an aberration.
edit: no online sources? I don't normally pay $35+ because a hostile, anonymous internet commenter said something would refute someone I respect but didn't want to explain the ideas himself.