My son played for what is probably the only HS in America to have 3 first round draft picks and current Major Leaguer's as well as a good number of other good college level players transfer out. It wasn't the coach was a jerk or anything like that, he just played players by their grade, not their talent and you didn't play varsity till 11th grade no matter how good you are. Imagine a first overall pick playing JV in the 10th grade. In 5 years on the team my son played in only 12 games at the varsity level in his true position, catcher. He was forced to pitch, play first and DH because all the other good pitchers left, there wasn't much talent behind him either. Several local colleges came to look at him and told him he could walk on in the fall but they didn't think there was anyway he'd make the team and encouraged him to go elsewhere. His coach even told him one day some college kept calling and leaving messages on his phone asking about him, did he know what they wanted? He never even called them back. He did play for a top showcase team in the summer but nothing ever came of that either. He ended up with a D3 coach he was taking hitting lessons with making a call to a D1 JUCO. After one year there and being named first team all Region catcher he had a number of D1 offers including an SEC team, an ACC team and several mid majors, even one of the teams that told him not to bother walking on offered him a full scholarship (it was a very low rated academic school and he would have gotten academic money as well as baseball money). The coach said he didn't know he could catch and hit like that. He accepted a mid major D1 in the state and did well, even lighting up the other school that rejected him in 3 out of 4 games they played against them. He went on to become a first team all conference catcher and was drafted. He has just finished 4 years of indie pro ball.
If I had to do it again I'm not sure I wouldn't do the same thing, it worked out well for him this time, and moving just so your son can play ball is expensive, but I definitly think he should play HS ball, just don't get hurt.