As someone who is relatively young right now and has had a Skymiles account since I was 4 (and AAdvantage since 12ish?), here's what they did:

Until I was about 15 or 16, my parents would use the miles to buy tickets for family trips and such. But once I got to that age, I started learning more about the miles/points game on my own, so I started having an opinion on the types of tickets that it was "worth" using miles on as opposed to cash. Not entirely because I would "get" the miles once I turned 18, but it might've played a subconscious role. Since I wasn't traveling much in High School, I tended to use what few miles I had to position for cheap cash JFK-Europe trips. And now I use the leftover miles and whatever I've accrued since for whatever vacation I want.