This is not a new policy and is not unique to Wake Forest. My child applied to 16 schools two years ago and at least one other had a similar statement but I don’t remember which one. In any case, it can be an issue at schools that are need-aware for admissions. About half the schools my child applied to are need aware for admissions, including Wake. (though she ended up at a school that is need-blind for admissions).
Even at Wake or any need aware school you can still in subsequent years submit a FAFSA and could be eligible for Pell Grants, and Federally subsidized or Direct unsubsidized loans. I read this policy to mean you would be unlikely to receive need-based institutional grant aid…but note that they hedge and say “may” be precluded… I think the issue is really one at schools that are need aware for admissions.