Evolutionary competition is cut-throat because the losers die in nature. Human societies were supposed to be progressive in that we saw ourselves as people, not as animals. We progressed in certain ways but in others. For instance, although we often came to each other's aid in societies, and developed sophisticated cultures that were meant to uphold certain ideals, we ended up living in dominance hierarchies (feudal kingdoms and empires) that reflected the natural social organizations in the animal kingdoms (pecking orders with alphas hoarding the resources). The majority were ruled by a minority of powerful and wealthy people.
Modern society was supposed to be more progressive than monarchies. As you say, everyone was supposed to benefit in that capitalism was supposed to promote the interests of a middle class of merchants, to raise the living standard for everyone. And of course, capitalism does have its efficiencies.
But as we learned over the course of modern history, capitalism ends up succumbing to the same natural law of oligarchy and to the same power dynamics that mock our distinction between people and animals. Witness the plutocracies, the enormous concentrations of wealth in fewer and fewer hands, the rise of monopolies, the promotion of psychopaths to positions of power (like the kings and emperors of old), and the capitalistic capture of democracy.
How do you know the "purpose" of capitalism? Where is that purpose spelled out in such a creed? The hope reflected in the early attempts to sell capitalism spoke of the "invisible hand" that was supposed to benefit society as a whole. And capitalism was part of modern individualism which implicitly saw all humans as equal in their personhood. But how do you know that that original selling point wasn't belied by an unstated purpose? Or how do you know capitalism achieves that official selling point? Maybe the initial expectations were naïve, and capitalism ends up generating plutocracies that resemble neofeudal kingdoms. Maybe social democracies recognize that fact, which is why they dismiss libertarianism (classic liberalism).
There's a big confusion here that illustrates my point about the slipperiness of these concepts (self-interest and selfishness). You say, "I don't believe for a second that you respond out of a concern for my interests. Like myself, you get something from them."
So you're equating taking someone else's interests into account, with acting altruistically in Rand's sense of sacrificing my interests entirely to help someone else. But acting out of self-interest can be of mutual benefit. So I could be respecting your interests by responding to you, while also acting out of self-interest (rather than selfishness), getting something in return by responding to comments. I never said I was being selfless in a saintly or "altruistic" way--although frankly I don't know if anyone benefits from these comments, least of all the author who would rather be writing articles. I respond to comments mainly to be polite.
When I write these comments, I speak on the basis of the hundreds upon hundreds of online articles I've written since 2011. My arguments are mainly in those writings. Besides the ones on economics and Rand, I've written some specifically on libertarianism: