Pitching under-handed is against the rules in baseball.
Sidearm and submarine pitchers (I think) have had relatively good health. It is much closer to the more natural underhanded motion. It is just a more difficult pitch to master (control-wise), and I think also limits your number of types of pitches a bit more. When I was 10-12 I would go submarine 2-3 pitches an inning, with success. Regrettably I had a coach (from 12-15) that told me not to throw that pitch. I never developed any off-speed pitches (other than a decent slider at about 14) to go with my fastball, which made my fastball more hittable. Having that as an option would have helped. Obviously a sidearm/submarine motion isn't going to fool any hitter, but it does take an adjustment (like a knuckleball).
I do think teams "baby" pitchers too much now. And what has it gotten them? More elbow problems than ever before!!! Granted I am an N of 1, and was never MLB quality, but I could throw pretty hard (60's when I was 12, around 80 by 15). When I was that age, I would throw 50+ pitches at home an hour or two before I was to pitch a game each week, would then go out and pitch a complete game, throwing probably over 100 pitches each time. Then at practice I was usually the one throwing the most batting practice (except I didn't let up much). When I was 15 I pitched on the HS varsity team, and then when HS season ended I played in the 13-15 yr old league where I also pitched. I tracked my stats that season and in every one of those starts (one each week) I threw 110-135 pitches. I felt the more I threw the better.