Sounds like Questbridge National College Match. However, Questbridge is for students from low income families, which the colleges will offer their maximum financial aid to, so financial aid and net price differences between schools should be minimal and therefore not so much of a concern.
But something like that could be worth considering within a state university system with fairly uniform need-based financial aid policies, although it could not be binding because students may also be considering private and out-of-state schools.
Another idea to make it work would be for students to apply for financial aid first, with the colleges delivering binding (to the college) financial aid offers (conditional on admission and matriculation). Then the students can use these offers to determine their preference ranking (or not rank at all any that are unaffordable) in a match system.