Probably not, but it would pay for some fairly hefty mental health services. Thinking of the local high school closest to us, the football team alone has one full time and three part time coaches, uniforms, equipment, travel and let’s not forget - a stadium. Not having those expenses would easily cover 1 full time psychiatrist and 2-3 supporting psychologists.
So I can see the OP’s sister’s position that instead of having a small staff of mental health providers, a school has a sport that only boys can play, that is known to cause long term brain damage, that is not a “lifetime” sport that people will play for years after participating but gee is it fun to watch… Maybe not the best choice for taxpayer $$$.
On the other hand, even though this one facet of the discussion (does it make more sense to spent school $ on football or mental health) makes sense, I’m not convinced I want the put mental health services in the hands of government or schools for a variety of reasons.