I personally have no PRO'S or CON'S with respect to play or train. Here is what I have witnessed over the years:
Some coaches in organized amateur ball have a sensitive issue with players that receive serious private coaching. Why? Because they feel that part of their control, not to mention game knowledge, has been taken away by someone other then themselves. These coaches operate in "my way or the highway" environment.Also, some amateur coaches like to keep their talent close, with "eyes' only" in their domain.
By not playing organized ball your son may miss out and being seen in an organized ball context. In that regard, Steven Ellis gave you solid advice when he mentioned the priorities of play Vs train.
I too totally get your disappointment and frustrations. Amateur baseball is plagued with the conditions that you itemized and it's been that way for decades, and will continue regardless of who says what.
Travel teams, elite teams and so forth have at their center of gravity the foundation of what you are now experiencing. There are exceptions to be sure - but those exceptions are far and few between.
So, think this out, slug it out, grind it out, and do the best you can. And if all else fails, this situation weighs on the youngster more that it does something for him and his sprits, look elsewhere where he can have a good time, enjoy the game for the game itself and then call it a day. If this is not a "can do", there's more to life than playing baseball. In fact, there's scouting, 4H, FFA, amateur radio including CB radio, get an old jalopy and take on a father and son car project, joint a sportsmen's club and shoot off some cap and ball black power - a neighbor of mine and his two sons joined a Civil War reenactment club and shot everything from black power canons to Colt-Patterson cap and ball revolvers. They never hit anything, but then with all that smoke no one could see any how. Take up fly fishing - just be careful. I had to have nine stiches from a hook that a guy sunk into me.
If you and your son are using this team as a vehicle to get into college or some other agenda - obviously it's not gonna work. On the other hand, stranger things have happen. So, I would suggest regrouping, talk this through with your boy and see if this is worth all the persuasions that your son is experiencing and what's expected as a payback.