That's a theory of parenting: attachment parenting. Even AP parents gradually introduce time away from their kids as the kids get older. Well, all but the most fanatical, and those, well, see above re: attending job interviews.

Putting aside the first few months, which are called the fourth trimester for a reason, every parent I know (really know, not just chat with at school activities) has had something in their lives that doesn't revolve around their kids, even if it's just following a tv show or watching sports (both of which seem to be acceptable to the same people who judge parents for playing an RPG once a week). Of course, every parent I know, I know through something I do that doesn't revolve around my kid.