^This is what most schools do. They read applications without regard for need, then do their admissions based on what the school can afford, making every effort to offer FA packages that will make attendance possible.
My guess is that at the fringes (including WL), ability to pay is a major factor but that for most of the class, it is not. Many of the “institutional needs” naturally favor kids from wealthier backgrounds, so this often sorts itself out in that arena.