NFL have an anti-trust exemption. It can be revoked. Congress has actually already considered revoking it in the past. If they did revoke it then those salaries would come down on their own.
The sad part of this is the right wing is quite well aware of why they are paid so much, but the left wing are mostly oblivious. Keynes once alluded to this when he said "practical men who believe themselves to be quite exempt from intellectual influence are usually the slaves of some defunct economist".
The truly sad part is that this isn't just about football coaches. If you find somebody who is paid outrageously well while others are paid really badly it's usually because the rules of the game have shifted such that one party is forced into brutal competition while the other is mostly shielded from competition.