My son attended a large classification high school. They were a good team winning two conference titles and a second over his three years. In that time only two pitchers also played a position. The biggest issues for all those pitchers is they couldn't hit and weren't that good in the field.
in his soph year the center fielder was a starting pitcher. I believe another could have been the DH. But he was slow afoot. Plus he hurt himself by constantly irritating the coach (when his father wasn't irritating the coach). He was ultimately kicked off the team.
My my son was the closer. He came from the field. Soph year he played short. Junior and senior year he played center. He would warm up between innings.