It may be the case that unless a private college explicitly states that they don’t consider financial need, then they’re likely to do so to at least some degree.
I have never worked in college admissions and have never spoken to anyone about the topic who works in admission……But from living in a large city with academically rigorous public schools and elite private schools, I think even the schools on the list of 12 top need blind schools likely game the system. In other words they know that kids paying 60k for private school are likely to be full pay vs a test in school with 60% free lunch. They take kids from the big, academically rigorous schools but - in my view from mere observation - not at the same rate as from the private schools. My kids did fine in admission, one from private and one from public but I think the schools do know they need full pay kids and these kids re more likely to come from private schools generally. They have also received great educations and can do the work so not getting in b/c they can pay as they are certainly very talented, great kids. Nonetheless, the game still has some built in advantages for those that have markers that they are likely full pay.