our college coaches both wanted us to ice, but the guys who wouldn't would just walk to the trainers w us and just not put any on. Strongly encouraged but not enforced.
In terms of ice baths, I have taken a couple. Im hard pressed to think of any time a baseball player would take one without it being overkill. Only thing I can think of is maybe a hardcore offseason workout. And by that i mean cross training, plyometrics, weights, sprints, etc, full intensity, all in the same day. Even then, i dont think it would be worth it cuz they suck, bad. And in that instance, youre in the offseason so its not like you need to bounce back quick for a game or anything
I played basketball in HS, so I can see the demand for that especially after logging 40 plus minutes a night on a consistent basis.