My son is both a pitcher who has pitched a lot at all levels. He is also a hitter who switch hits. He wears the protective gear as a hitter to avoid being hurt, especially on his pitching elbow, not to lean in.
As a coach and a dad, I think all pitchers should wear chest and head protection and all batters should wear protection. Let's be honest. Very few high school batters are willing to lean in on your son or mine. My son has been hit 10 times so far and does not like it but also does not feel that most are trying to hit him. They are trying to pitch around him and make him get himself out and the pitchers just throw the curve or fastball in a little too close. He crowds the plate not to draw walks but because the umpires are not the best and he loves inside pitching so he hopes the pitcher will try to pitch inside.
Hitting batters is part of the game, intentional or unintentional, but it should never be at the head. Throw inside waist high or down to move a batter back but never up to move a batter back. I believe any pitcher who is deemed to throw at a batter's head intentionally should be suspended for a long time. No place in baseball.