We clearly have different expectations of family. If I was living with friends, I'd want to contribute something (though would not in the least have the same expectation if a friend was staying with me for an extended period of time (to distinguish from having a room-mate which is a different situation)), but with family? I'm pretty sure all of my family, including extended family, would be offended if I even offered. At the most, they'd accept a dinner as a thank you.
Personally, I respected my father and as such wanted himto respect the fact that as a man earning a wage I wanted to contribute to the household. He didn't "need" my money, but he accepted it as the good gesture it was.
The notion that family is there to free-load from is always amusing to me. I love my family, so I supported them within my means. It did not detract whatsoever from our relationship, and the notion that it could is pretty ludicrous. If anything, it strengthened it.
Let's not confuse generic 'wage-earning adult' with your own children. If Fred Bloggs wants to live in a property I own then yes he can pay, but there's no need need to charge your own children a pointless and tokenistic sum for what amounts to tens of thousands of pounds of benefit under the guise of teaching them something worthwhile.
Yes, lets not confise a wage-earning adult with... a wage-earning adult who happens to be your offspring. Because clearly that would be crazy, seeing them as a wage-earning adult.