Pitching is a specialty that requires a coach who understands it. I've seen coaches who don't have a clue about it. I agree with your opinion on school sports, but if the school coach can't provide the level of instruction needed for a pitcher to be successful, he/she is hurting the team by not allowing the pitcher to get that instruction. One day a week is not too much to ask. It's really not different than a school coach who can teach pitching taking the pitcher aside one day a week in a school practice for individual instruction that does not apply for position players.If he lets her miss then he has to be okay with letting everyone else miss. And then you end up with not enough girls to hold a productive practice.
Does she enjoy it, is she having fun? If so let her play, if not let her quit.
Personally I think playing school sports teaches a valuable lesson about learning to deal with adversity and not always getting to play where and as much as you think you should. Come college it’s a skill not enough players have