It's not just the fastballs that are/were getting people, it's the strain on the arm doing an unnatural motion while throwing a curveball.
For every Bob Gibson or Greg Maddux, I can come back with a Kerry Wood (who's arm couldn't stay healthy but had one of the best curves I've ever seen) or probably the most famous being Sandy Koufax, who retired at 30. Hell, when I coached little league, I wouldn't let kids throw a curve because I didn't want them to mess their arm up while still developing. That's not, or wasn't done, by everyone in the league.
No matter how you slice it, this isn't 40 years ago. They start training younger and specialize a lot more in one sport. Every arm has a clock. There's no reason to speed that clock up when it's not necessary.