I'm no expert on baseball, but I am a father and so I'll come at it from that perspective.
I think the coach messed up big time. Like you said, the coach dumped him in the outfield then when he was out of options, needed your boy to play 3rd. No coaching, no practice, just handed a new position. The coach needs to take responsibility for coaching his team and he failed the kids in this respect. You mentioned that others kids have stopped turning up, that seems like an indicator to the coach's ability to motivate the whole team.
When it comes to sports, the dad is the child's agent and you have to look after his best interests. If he is so demoralised he doesn't want to play, then no way should you force him to play, if he doesn't want to play for this guy, see if you can get him in another team. As I see it, the coach has already broken the commitment, it's your son's decision whether he wants to play for this guy anymore or not.
It's a valuable lesson either way. to follow through a commitment not just to the coach but to the other kids on the team. Or, to have the guts walk away from something that isn't worth the hassle it causes, it's a lot easier to bow to the pressure to stay than to have the guts to actually quit. If your son's playing out of obligation rather than fun, then he really needs to question if his time wouldn't be better spent doing something that is ultimately more rewarding whether it's schoolwork, family time or another hobby.
Either way though, try to put a positive spin on it for your son, so he can see the benefits and the consequences of each option and support him whatever he decides.
From my point of view though, he owes the coach nothing at all anymore, the coach let him down by not coaching 3rd base properly, there's no "instinct" about it when you're 11. Props to you for keeping out of it though, prsonally, I'd not be able to keep calm and would have had "words" with the coach and specifically sought out one of those "heated moments between parent and coach"