Must admit... I am guilty of too much baseball. However, I enjoy getting away from it at times. Two of our kids loved the game and couldn't get enough of it. They weren't told to stay away and take time off. Our other two kids liked baseball but they liked other things much more. I never told them they needed to take time away from the things they loved. But all four on their own figured out when to take time off. No one was pushed to do too much or too little when it came to sports or other activities. The only pushing came towards academics, behavior and honesty. It is well worth it if you have to help/push someone to be a good person.
So I see this as non issue. So what if someone burns out, why be fearful of that. We all burn out from different things. Usually when something is no longer fun or you can't be successful enough. I believe burnout exists, but if it happens it happens. If a young baseball player burns out on the game, I would think he would have burned out later on anyway. There are millions of people working who were burnt out on their job a long time ago. There are others that absolutely love what they do every day. Nothing to worry about, sometimes changing interests ends up being the greatest thing that's ever happened to a person.
Everyone knows this... There are many much more important things in life than baseball. Does anyone get concerned if their kid gets burned out at skydiving or playing checkers? Anyway, IMO, it's possible that you could cause a child to get burn out by forcing things, but you can't stop someone that loves it and isn't burnt out. They're usually the ones that hit it big.