My son's pitching coach will teach pitchers curve balls when they can demonstrate a repeatable arm slot and consistant body control. He has taught it to 10U players with success.
He made my son wait till 14U because he simply didn't have a repeatable delivery.
I agree with the comments on strikes. I also believe the first offspeed pitch to learn is a change. I believe a properly thrown curve ball is a safe pitch. I believe an IMPROPERLY thrown curve ball is a dangerous pitch. I believe mechanics break down when a pitcher is tired and the ability to throw a curve ball with good mechanics gets dangerous when the pitcher gets tired.
My son's pitching coach was a MLB pitcher who threw FB & Chg. He also had Tommy John surgery. He'd tell you that FB / Chg is supposed to be safe and that the definition of a bad pitch for an arm is the last pitch thrown before an injury occurs and that isn't the root cause of the problem.
If the kid can throw it with good mechanics and was properly taught, let him throw it. 10 curves a game? I don't think its a big deal, as long as he's doing it correctly. 40 curves in 60 pitches? Probably a bad idea. They should learn to throw the FB and work off that with the change up / curve. Most MiLB programs work that way, so 13U shouldn't be any different.