For me personally,I dont think children have any business being close to the world of Bitcoin not because Bitcoin is bad in itself, but because of the various vices they might be exposed to along the line which they might not be matured enough to handle. Among such things include gambing, falling for cheap scams, HYIP sites with exciting bogus rewards among other issues even as adults face in this crypto-world.
I wouldn't worry about these things. I've done all of those and I've moved on. Everyone is capable of doing that. We lost our money by gambling and from HYIP sites, and that served as a lesson to all of us. One thing I would worry about is what if the kids started working continuously. If I had the time, I wouldn't do anything else but continue exploring the bitcoin world as this has much more opportunities than the job offerings in my area. People's nature is to be greedy and once kids become exposed to the world where they can make good amount of money, I'm afraid that their greed will eat them up.