Most HS coaches I've seen would have pitchers hit. But I know there is a difference between a DH/P and a P who plays another position. I am surprised coach is limiting things and agree with Shoveit4Ks--are the other players better. For the OP, some HS players select a travel/showcase/Legion team where they can display other tools, play other positions. If your son wants to be a 2-way players in college (and showcases really well) there are schools that will welcome it. Probably more common at schools with smaller rosters.
Son had a college teammate who was one of the leagues top closers(good fastball, slider occasional 93MPH, and power hitters. He got hurt his senior year, and is now a graduate student at a P5 with his 4th year of eligibility. He's pitched in relief, 1B,DH and currently (it's early) has team's highest BA.