As a former baseball mom, the same can be true of the repetitive line drives to the head. If you are taking that many, you shouldn't be pitching...
As a parent of a catcher who repeatedly has to "drop and block" aka take balls to the chest/stomach, fear and mental blocks absolutely are a thing. He spent ALL last year refusing to block, and it was a major issue causing tears, anxiety, and doubts. I think this tendency to say gymnastics is scarier or harder or whatever than other sports just is a horrible path to go down. Why does it have to be a comparison? Look, my son practices baseball stuff at home (hits off the tee primarily) and he is in practice some weeks more than my daughter who is part of a level 9 acro pair. That said, my daughter is on her blocks at home for hours on end. She has an air track (GASP, I KNOW) - not for practice per se, but for her enjoyment. We don't critique EITHER of them at home or in the car after practices or games/competitions.
I do stay at practice, largely because it's too far to go home and come back, and leaving means I'll spend money I don't need to. Sometimes there's errands, but mostly I work, socialize, or watch movies/tv or read. As for the longevity issue - if my son decided to give up baseball I'd feel the same as if my daughter gave up gym. It's been the primary sports focus in his live since he was 3. Yes, he plays other sports (and DD has other activities, including leadership, a few seasons of soccer, etc...) but it would be a big shift for him and I would want to make absolutely certain he was sure.
I will say this too, as a kid, my parents let me switch gears regularly. I finished whatever I was committed to, but I danced, I twirled baton, I played the flute, etc... And as an adult I feel like I never got the chance to truly become great at any one thing. Part of our jobs as parents is to help our kids make decisions that aren't based on whims or one time frustrations - to see their long term goals realized. I never got that, and while I'll support my kids giving up their activities/sports if that's what they truly choose (DD has done artistic, T&T and now acro), I will be sure that they aren't sacrificing long term goals for short term frustrations. And part of that is not being the de facto coach once we get in the car, whether it's gym, soccer, baseball, music, whatever.