Does bench pressing hurt the shoulder?
If done incorrectly, yes. Just like if you squat incorrectly you can hurt your knees, and if you deadlift incorrectly you can hurt your lower back.
No exercise is inherently evil, it comes down to how you’re doing it. Because any movement under load, done incorrectly, is a recipe for pain
With the bench, look first at the athletes technique, everything from setup to takeout, to bar path
Then look at the program itself. How is the bench being progressed? What is the volume and ratio of protraction to retraction?
Also consider individual differences. It’s not appropriate for every athlete to bench with a full range of motion, nor is it necessary: they’re not competitive powerlifters
Put all that together, and then according to the research, bench is one of the BEST exercises for driving performance on the baseball field (1).
So it’s not WHAT you’re doing, it’s HOW you’re doing it.
Kazuyoshi Miyaguchi et al. Relationship between upper body strength and bat swing speed in high school baseball players. Journal of Strength and Conditioning Research: p 86-91. July 2012