I grew up in SOuth AFrica, where there is a culture of sport in schools. EVery child was obliged to participate in one after school sport in the summer and one in the winter. For the non-sporty, this was social tennis, social badminton, social swimming etc. For the more sporty, there was hockey/competative swimming, rugby, football, gymnastics, cross country, athletics, badminton, netball, basketball, volleyball....
In winter, I trained twice a week and matches on Saturday mornings (hockey) and also did volleyball all year and swimming every week for 1.5 hours (as well as swimming at home) My brother was very good at cross country and eventually joined a local running club after school.
There were obese children, but exercise was mandatory at least once a week.
But...the teachers took on the extra curricula activities - the male teachers gravitated towards Rugby (it is more a religion than a sport) and the PE teacher ran the hockey/gymnastics and netball.
Other teachers with specific interests would run a club - so a runner teacher would take the opportunity to run with a group of teenagers twice a week - it was his great love, so no great chore. Ditto the badminton teacher got some great games with his students.
They werent, overall, professional coaches, just teachers with an interest in a sport.
It helped also that the school day was from 8am to 2pm, with short breaks, so that the sport could be done immediately after school and teachers still had time for a social life and marking/planning.