I get the feeling that YC is based on a different set of values and insights than your typical VC firm is. Just my impression, of course, but I get the feeling that PG is trying out a social "hack".
There's a magical section of life that a lot of people don't take advantage of - the first few years out of college, when your responsibilities and personal needs are very, very low. A lot of people in their early twenties who don't go directly to grad school spend this time as paralegals, programmers for bigCorps, and so forth.
In a way, YC is testing out a perfect hack - showing how a remarkably small amount of money, along with just a bit of encouragement, can completely alter the course of a lifetime - and, if it is successful and spreads as a model, ultimately change the nature of careers and work.
It's not that married founders with kids and a mortgage can't participate, but if "married with kids" describes you (and it certainly describes me), you probably aren't in that state anymore. But it's up to you to decide - I do know a startup founder who is 40 with a wife and little one (his wife works, though, which helps a lot - though in this case, the few grand YC offers would be irrelevant, and he's funded through a more traditional investment approach). I know lots and lots of married programmers with kids who work as early employees of startups. I could recommend this, because if you're very skilled in Silicon Valley, you can probably get a new job quickly - but it's probably nothing like being in YC.
I remember my first few years after college - I lived near the beach in San Diego, my rent was about $325 a month, and I surfed constantly. Then I went to grad school. Wouldn't have been a bad time to try a startup, I suppose.