It could be happening via investors, though. It could be that e.g. Google decided to go for the big time partly because there was so much funding available in 1998, which in turn was true because investors were hoping for IPOs.
You haven't seen them say it directly, but how many applications do you get that are for fairly ambitious and big projects? What percentage are front-end heavy web-apps/aggregators? What percentage are fairly ambitious and require a serious research, development and have a huge potential for growth? That's a question you may be able to answer better than anyone else (although I'd imagine most YC applicants are a self-selected crowd and those hoping for an exit other than M&A and to hire a great deal of talent may not even apply to YC).
I also didn't think about the investment angle at all. I wonder how much investors are pushing for companies to sell quickly vs. grow.
I'd say many if not most of the startups YC funds have the potential to go public, if the founders were sufficiently driven. (In saying that I'm relying on the fact that practically no companies that go public look like they will at the start. Apple started out as a company that was going to sell plans for computers.)
Wow that's something I haven't entirely considered, despite knowing it to be true. Somewhat adds to my argument, however, without the chilling effects of regulation we may have seen a more interesting and diverse market -- but now I am in purely speculative realm.