> natural solution would be to increase the number of teams

Reminds me of my dad (b. 1945) talking about his HS sports experience in the early ‘60s at a large (~3500) Southern California public school. Not only were there varsity, JV and frosh teams, in high-interest sports like football and basketball there were multiple teams for every grade. Competition was still high if you wanted to play at the highest level, but if you wanted to play, there was probably an option for you.

Public schools are simply not funded the same way today