The US Army introduced fitness tests in 1943. They have relaxed their standards since.
When I began high school, every entering boy had to take the test while the coaches recorded. They were looking for athletic potential. If you didn't pass, you had to do a semester of remedial fitness before you could even do a (required) intramural sport - or even a JV sport. The remedial fitness was a bitch. 2 1/2 hours each afternoon. Ex-USMC math teacher was the coach. He made overweight kids go on diets and run extra unless they needed a JV fullback. Good stuff if you could handle a little humiliation. Runs, sprints, lifting, squats, football sleds, sit-up marathons, pushup marathons, etc. I flunked on the pull-ups. They also had a swim speed test which I handled easily but I didn't want the swim team. I still stink at pull-ups.
Are You As Fit As a World War II GI?
I doubt that a public school could make such demands on kids. Funny, as I reflect on it: We had riflery and shotgun teams too, but they were extracurriculars, did not count as sports. Still do, I am sure. Heck, even girls' summer camps have them today. A Bird Dog daughter was an NRA-certified riflery and archery coach/counselor at a girls' camp.