I laughed out loud when I read, 'I don't think anyone thinks of ourselves as "people, not as animals." We are animals.'

I dare you to call everyone you meet an "animal," and see what happens. Say to a stranger, for instance, "Come over here, animal."

Biologically, we're animals and more specifically mammals and primates. But we're primates that evolved personhood, which makes for the distinction between animals and people. We're domesticated rather than wild animals, so we think of animals, as such, as being different even from our pets and livestock (from our fellow "family members" and private properties).

But that crude reductionism seems to play a Nietzschean role in Rand's advocacy of capitalistic "ethics."

You strawman my view when you say, "Your picture of Capitalism as a tool for ruthless men to grab the riches of the populate fails on so many levels." "Tool" is your word, not mine. And I never said capitalism benefits only the wealthy few. What I've written is that capitalism enables the wealthy few psychopaths to dominate as they've always dominated even in other economic systems, despite the early-modern promise that capitalism would be more humanistic and progressive than medieval feudalism. Libertarians buy into the early promises, ignoring the results of capitalism, whereas socialists say we should learn from the history of capitalism and regulate this system to counter its inherent flaws.

I spoke of cut-throat competition in nature, in response to your point that competition is everywhere, even in the wild. My point was that human competition should differ from the cut-throat kind that exists in the wild, because civilization is supposed to live up to the ideals we set for ourselves. The selling of those ideals is everywhere, in religion, philosophy, and art. Culture is the celebration of our ways of life, so we implicitly think human society is better than life in the wild. That's our Faustian bargain with agriculture and with other technologies.

If your question is whether there's a utopian system that prevents cut-throat competition, I don't know of any. But that's a red herring since there are degrees of inhumanity we're willing to tolerate. The social democracies that subscribe to the Nordic model are more communitarian and less individualistic or "cut-throat" than the democracies that belong to the American model. Libertarians need a way to overlook the cut-throat aspects of the American style of capitalism, so they blur the distinction between animals and people, for instance, as you did. If we lower our standards in that way, we can overlook the inhuman, self-destructive downside of American, libertarian capitalism.