It looks to be a mixed question. High School? How big a school? Summer is different. My son was, for all purposes a pitcher only on high school varsity this past year because the team started 8 seniors. However, he still picked up 10 PA's. Other than him, all the pitchers started in the field when not on the mound. Our HC does prefer, though that his infielders other than first and catcher don't pitch. Next season, my son will start in left when not on the mound and most likely hit clean up. It's a Colorado 3A school of a little over 600 students.
I think with bigger schools it a lot more prevalent, not because they are trying to save a kids arm, but because, due to numbers and talent, there are probably better options in the field and at bat. Smaller schools don't have that luxury.
Summer can-and usually is - different due to the concentrated talent level. Except for the occasional stud, most good summer programs will have better options. So, it would be rare that a kid good enough to start on the mound is also good enough to win a spot in the batting order.
Just looked back on maxpreps and my school hasn't had a true PO as far back as I look.