True recent anecdotal story...
I coach V. Last night, we had both V and JV squads gathered together waiting to have team pics taken. In an effort to provide some guidance to the JV coach, I asked the JV boys which of them were pitchers. There were ten. At least nine of the ten are truly potential contributors on the mound for V down the road and it is too early to rule any of them out. We play two games per week. (Keep in mind that Frosh/JV ball is supposed to be largely developmental for V). When one of those nine pitchers starts a game and is doing well and he continues to ask for the ball again next inning, what do you do as a coach? You sure as heck don't want to discourage that "give me the ball" attitude but you have nine other guys and you are trying to allocate the remaining 10 or so innings left for that week. These are the types of things that most parents are not aware of when playing time and position decisions are made at those levels.
That said, should your son be trying as hard as he can to make it really difficult to take him off the field and/or out of the lineup? Absolutely.