Congrats to him on two terrific choices!
I have a bit of a different take on the "go where you would go without baseball" thing. Academics are very important. Being in an environment where he can be comfortable and happy is very important. For different players and families, other things are very important... maybe proximity, weather, costs, etc. But baseball players are going to spend a HUGE chunk of time with baseball. The team, the coaches, the facilities, the gym, etc. I don't think a player should make decisions based on the possibility of an injury. JMO.
Sounds like "A" has become a terrific option but, of course, the big fear is that college coaches tend to be very mobile (particularly good assistants) and those coaches are the biggest selling point for your son.
You said... "He would never consider this school with other coaches or without baseball."
What are his/your thoughts if you shortened that statement to just... "He would never consider this school with other coaches." ? Because this may be the more likely scenario.
Considering he likes the other school better, I don't know why you/he wouldn't allow that to play out and see everything they have to offer. They surely can't be naive enough to think they are the only ones interested in your son if they think that highly of him to communicate what they have to date. Gather all information before making the big decision. Sounds like they have afforded you time to do so.