It not that big a deal with a 1HBH. It's easier for most people to learn with a 2HBH, but a one-hander can deal well with high balls.
You do need strong shoulders, that's for sure, since you don't have a left hand to help out.
I find it's easier with a 2 hander to hit down on the ball aggressively, whereas with a 1 hander you generally have to hit a loopy moonball, or slice down on the ball. That's if the ball is extremely high up.
It's just easier for kids to learn a 2 hander, because they generally aren't strong enough to properly wield a racket above their shoulders.