Addressing this specifically:

"In practice, I'd have to say that free-market capitalism increases wealth disparity, or at the very least fails to decrease it. (Socialist systems decrease it very bluntly by direct redistribution of wealth.)"

So do you favor socialistic blunt force redistribution of wealth, or do you think there are other options in a free-market capitalistic (which I would argue the US is not) society that would lead to lower wealth disparity. It seems to me that competition of the free-market variety almost always ends up as a win for the consumer, and since this affects the poor more than the rich (they spend more of what they make) wouldn't capitalism tend to help the poor in the general sense, if not decreasing wealth disparity in the specific sense?

It's hard to talk about these things in an idealized world because that doesn't exist, but it seems to me that free-market capitalism would ideally decrease wealth disparity over time due to competition, but I'm curious as to your thoughts.

Keep in mind that I think the US is a poor example of free-market principles in action, or at least in some industries.

The other thing about socialism decreasing wealth disparity seems to be at least a little counterintuitive to me. I'm having trouble verbalizing why it seems wrong to me, so I'll come back to it later.