Yeah, that’s how my high school worked too- the vast majority of teachers also coached some level of some sport or other, and the vast majority of students were also involved in some sport or other. Not everyone, as it wasn’t compulsory, but it was probably 60% of students who were on a sports team of some kind- we had football, basketball, baseball, soccer, golf, tennis, cross-country, track, swimming and water polo.
But we were a school of about 650 all-male students, so there was a lot of opportunity- not all teams had entirely full rosters. But had you doubled our enrollment, we’d have had full rosters, but the percentage of students involved in athletics would have gone down as well.
Generally speaking, the dedicated coaches taught PE and/or Health, while the academic teachers were generally either assistant coaches or coached JV or lower level teams.
I think it was a good thing- we didn’t have a jockocracy, as most people were involved in sports, and it generally made for a more school-engaged student body than I think we’d have had otherwise.