I had this same thought at one time.

Ended up being the best cruise I've ever taken and the experience wasn't anything like I had expected - to include your thought of 3000 kids running wildly about, primary colors at every turn and not being able to turn around without bumping into some character.

They do an EXCELLENT job of keeping certain areas of the ship 'adult' only - and they mean it. I watched a few crew members get a couple of 15-16 y/os out of the adult pool area. There was no turning a blind eye to it.