There are so many factors that contribute to success, and they are never all equal, so any sort of up-front filtering based on some factor you think is correlated with success is going to miss out on people. And besides, I would strongly dispute any arguments that having a family is like some sort of handicap that must be overcome. In a lot of ways, I think having a family is a BETTER situation for starting a company!
My impression from reading YC's stuff is more that folks feel the value of the program comes to a large degree from the in-person interactions people have, so it makes sense to require people to be there in person.
Related, there's this scene from Moneyball, [1] that I love. They're all sitting around, discussing all this stuff that is at best tangentially related to _the actual things that matter_ for success of the team. It's very tempting and natural bias to latch on to this or that factor which you've become convinced makes a difference "all else being equal". But all else is never equal, and the question that is actually important is more the one Billy Beane keeps asking: "Yeah, but can he hit?"