I may be naive, but during my interactions with the NCAA and athletic directors, I never sensed that they opposed payments to players because it would divert money away from the schools or the NCAA. However well intended or misguided people may find it, the concern I heard over and over again was competitive fairness, and keeping an appropriate balance between athletics and academics.
It is true that athletic directors worry about their ability to keep pace with each other, so if one peer is building a new facility, they feel like they have to be able to find the money to do the same. That's an area where boosters diverting money to NIL deals could hurt, but I suspect most ADs recognize that if their well-heeled boosters provide NIL money, that is a competitive advantage. Conversely, I suspect most ADs also really like to be in control, so their lack of control over how NILs operate surely worries them.
I suspect that for most ADs who express concern about NILs, they are more worried about how other schools can get a competitive advantage over them, e.g., Michigan may worry that its boosters won't support NILs for their football players at the same level that Alabama's boosters will, putting Michigan at a competitive disadvantage in recruiting (I have no idea if this is true--it's an example; if I were guessing, I would guess that Michigan probably has one of the biggest pools of potential booster cash to fund NILs of any school in major college athletics).
