You forget that classes cost money, so do bikes, insurance (It doesn't matter if we never leave the ground, if a kid falls wrong and lands with a peg in his spleen it can still be a liability), etc.
If you personally wanted to organize something like that I would suggest trying to get in contact with a local YMCA, after school program, or something similar. Even then most of them would be very hesitant to allow something like that that.
Theres nothing you could get from a class that you couldn't get from just riding with someone better than you.