It's a weird essay. I think it goes wrong from the very beginning. From the second paragraph:
[B]y helping startup founders I've been helping to increase economic inequality. If economic inequality is bad and should be decreased, I shouldn't be helping founders. No one should be.
I think this is ridiculous. Creating new millionaires is not increasing inequality. I don't know anyone who thinks that (not to say that Paul might not have run into a few people who think that way). The problem, as you say, is the profound concentration of wealth into the hands of a few multi-billionaires. I would say also, it's the fact that the middle class in the US is actually shrinking.
The fundamental way that the wealthy can help the middle class, while helping themselves at the same time, is by investing in new businesses that create jobs. This is precisely what YC is doing! This isn't increasing inequality but decreasing it. Not only are they creating jobs directly, they're also doing so indirectly, by teaching people -- even those who don't get into their program -- how to start startups.
Founders don't get rich unless they build a successful business. And again, I don't think anybody minds that they can get rich; after all, a lot of them then either start new businesses or become angel investors themselves. There's nothing wrong with any of this, quite the contrary, and if Paul really does run into people who think there is something wrong with it, this is what he should tell them.
I would go so far as to say that YC and its ilk are among the most creative, hopeful, positive things happening in the US economy today. Though I'm not involved with them directly -- I haven't even worked for a YC company -- I am very glad to have them here in the Valley, and I'm excited to see what they do in the coming years.