A couple of points that I would like to make.
First, you have to judge each situation as it comes. If you ask the coach how he feels about private lessons and he has a problem with them and he is clueless as to mechanics, then you have a decision to make. if he is competent, then it is easier to follow his lead.
Second. Not many coaches that I see have the staff to run a proper throwing program for their pitchers. Not enough time, not enough bullpun, understaffed, not knowledgeable on how to run it, etc. I feel that if the coach is neglecting the kid, then it is up to me to get him the instruction that he needs. I personally would not hide it from the coach. During my sons soph year, I went to the coach and said that I was going to get him private lessons. He said he handled the pitchers. I pointed out that he not given my son a bullpen with instruction in 3 weeks. He had only told him to go throw with a ccatcher and a senior. I asked him if that was his standard method for handling pitchers. From that time on he gave him a bullpen per week. My quesion is would he have bothered had he not known my son had some talent.
Thirdly, (just an observation) most hs coaches lack the skill needed to take kids to higher levels. I would definitely get my child out of hs season lessons.
Good luck whatever you chose.
the Florida Bombers
"I love the HSBBW"