All my son's HS pitchers also played MIF, in the same game. There were only a few POs, and they did not play much. Starters did not play SS after pitching; the SS who pitched were usually relievers. Some starters did also play outfield when not pitching.
We had one catcher who sometimes closed. My son's freshman year, there was no other catcher who could catch him (threw very hard!), so he mostly didn't pitch. He pitched in college.