What level ball is the school? A pitcher is more likely to “maybe” DH when he doesn’t pitch at a D3. The general consideration is a lot of effort goes into being a pitcher OR a hitter and succeeding in college.
My son found it time consuming to focus on being an infielder and an outfielder. He was a utility player who started somewhere each game. He would get a run at one position when there were slumps or injuries.
When I played Legion (it was THE GAME then) the best hitter in the state was also the best pitcher. He got to college and never touched a bat. He pitched in the CWS and MLB.