Most of this is ancient history as son has been out of college baseball for three plus years now.
In high school, he was looked at as primarily a pitcher, and an occasional 1B/OF freshman year, until he hurt his arm pitching. He wound up having some surgery in the fall of his sophmore year trying to fix it, we moved in the middle of his sophmore year, so new school/coach, and physically limited as he recovered, sophmore year wasn't very productive. The new school though had a SS who also pitched, and a 1B that pitched. Junior and Senior years, son moved to the OF, arm was better, but not complete. Started a couple games as P, but as the season went on moved into closer role both junior and especially senior year. Different SS, but he was number 1 P and 1B was number 2, he and the other 1B rotated DH.
In college, one school had a P who DH'd when he wasn't pitching and occasionally played 1B. Son's freshman year was mostly as a relief pitcher, much to his dismay, only 10 ABs. Sophmore year, primarily DH/OF with only 3 pitching appearances. Transferred then, junior year, OF only, except he was pulled into an emergency relief appearance in a midweek game. Got the only batter he faced to pop up. That was the only pitching appearance by a position player that entire year. His senior year, there was no crossover. Which was pretty common.
Locally, a few years ago, SIU had a SS who was the closer as well. He wound up being drafted as a P, spent a couple years in the minors, and is back a pitching coach now.
High schools around here usually have few PO, just not enough kids.