Contracts would have to be part of the deal. Otherwise, this whole thing will just recalibrate itself and the same advantages/disadvantages will exist - just at higher dollar amounts.
Now: Pitt offers guy $100,000 in NIL. Michigan offers $200,000. He goes to Michigan.
If schools pay players: Pitt offers $100,000 base salary + $100,000 in NIL. Michigan offers $100,000 in base salary + $200,000 in NIL. He goes to Michigan.
If anything, the disadvantages will only be exacerbated, because Pitt may have to redirect NIL funding to it's general athletic fund (or consolidate them), whereas the BIG/SEC schools should bring in plenty of conference money to cover the "salary cap," and they'll be able to continue to encourage fan donations strictly to NIL.
Of course the other option would be that NIL is somehow wrangled into what it's supposed to be (market value for name, image, and likeness), as opposed to continuing to function as pay for play. But yes - without some form of contracts, I think this whole thing is incredibly stupid.