The universities do not yet pay the athletes. NIL $'s do not come from the universities themselves. The coaches absolutely have a say in who gets paid by whoever makes the payments (NIL collectives, individual boosters, maybe even businesses), but the money is not the university's to give. And it is not theirs to make public.
When (if) the House settlement is approved next week, that will change in some places and not in others. Then at least some of the numbers will likely be published by public universities. But that will only affect direct payments from the schools. NIL will still be private.