If what I’m hearing is correct for more than just my area of the US, the problem is lack of providers. I can suggest guidance take a look at Student A because I see something off, they can agree, but then they hit the wall and have to wait to see someone.
Even if every school were mandated to have a licensed Psychiatrist, where would they come from? A Psychologist can only do so much.
Coaches are everywhere and most don’t make a lot at my school.
AP, Special Ed, etc, is a school doing what they are supposed to do - educate the next generation to their ability.
I would cut sports before education. Not gym class or art/music, but extra curricular sports.