I think the question is very circumstantial. Health concerns (physical or psychological) can make it impractical and even unsafe for some children to live away from their parents. It becomes a different story when the child just refuses to work and settle on his or her own.

Society also plays a large role on what the "right" age is to leave and settle down on your own. In my country, it's not uncommon to find children (adults, really) still living with their parents even if they already have jobs. But I've heard that in the US, children can leave as soon as they hit their 20's (or younger).