It's a lot easier to get third-party investment once you've successfully sold a startup, and it's much less risky than pouring your own cash into your next venture. I'd say it's far from a foregone conclusion that you'd put a large amount of your own money in.
I'd have to add that YC isn't exactly your average startup though, and the founders putting their own money in sends a much stronger message of dedication to potential participants.
It would be easy to raise money if we wanted to, but we don't need it. The investment required is not so great that it's dangerously large for any of us.