Rocket,
I do believe that you have some very valid points. I believe also that the curve ball should always be taught but not necessarily as the third pitch, try it as the fourth, fifth or sixth pitch! True, we really don't know what breaks down the pitcher's arm eventually. 9 is just too young to worry about the cb.
In my son's case, they just felt that developing good mechanics, working on one's fastball and learning the change up over time was more important. And he too was very limited in throwing those breaking balls. Of course he had a change up, he threw it more in bull pen (after 15 on) and learned more to rely on his other pitches. He never felt that he was unsuccessful, in fact he loved having a good time with his different fastballs and then fooling them with the off speed rather than the curve. I believe that conditioning helps, but my son was very lazy with that concept, so I can never say he was the best conditioned on the team, that is why he remained healthy. He did work constantly on rubber bands and long toss, long toss, long toss.
The other kids who relied on the curves more often because they had a hard time with their fastballs just never made it due to sore arms, major injuries, just as some have stated here. Was it a coincidence, maybe, maybe not.
My son's pitching coach in college needed to work with him on his curveball more than any other pitch he had, due to the fact that I think, he just never relied on it that much.
Also during fall practice, the curve was very seldom used. One, they wanted the ball in play, and two, just no need to throw them in practice.
I don't know if you have a son or not, we are just trying to give advice that worked for us.
There are lots of parents here whose sons are playing beyone HS, would be interesting to know how the curve came into play when their boys were younger.