It’s complicated by the fact that if you do give the public schools money, they spend it on $10 million football facilities for 15 year olds, this is what happened in our community.
No idea about the specific situation in the US, but in my experience these kinds of distortions are almost always because said public school can only get the 10M for sports facilities because there is a specific fund for exactly this but not general school funding. The school then applies for it anyway because that means they can divert 100k or some other paltry share of said funds to be used for general school equipment etc.