I'm a family practice physician and take care of lots of kids and teens. I frequently see kids for sports-related injuries. I feel many of these injuries develop as a result of overuse. For example, the high school football team practices 3 hours/day plus a weekly game on the weekend. That's just way too much abuse on still developing knees, ankles, etc. Same goes for some young female gymnasts I see. They are just overdoing it and some problems show up now but I worry also about the issues that will arise down the line due to the repetitive microtrauma to their joints and muscles.
Another negative is that these kids are way overscheduled. They just don't have time to be kids anymore. All the time devoted to organized sports also takes away from homework/learning time.
When I was growing up, we played all kinds of sports in the street, at the local playground, in the schoolyard, etc. Very few of us played organized sports - Little League baseball was one of the few exceptions. Now, the vast majority of kids who regularly play sports do so in an organized league. More likely than not, kids don't play sports outside of those organized activities. They no longer play just for the sake of playing. It is no longer fun for most of them. And if you really ask the kids, most of them are doing it because their parents make them do it, not because they really enjoy it. Most would prefer staying home and playing with their friends.