I went to large schools for both MS and HS, and all of our PE teachers only taught PE throughout the day, as it was offered all seven class periods as there were simply too many students to only offer the class two to three periods.

In HS, freshman tended to have the largest class sizes as they only had two class periods to choose from, and were split between male and female. They'd rotate through all sports during the school year. All other years got to choose their class period and were able to select the sport(s) they wanted, and would rotate through different teachers quarterly, within that same class period, based on those selections.

Coaches that only taught electives usually rotated in teaching Health/Sex Ed and Driver's Ed.

I went to a small district where they shared roles. My wife went to a huge school where the PE teachers taught only PE and were paid coached as well.

In some districts, you need certification in a subject... a gym teacher can’t teach math.