Should I apply to elite schools?

I use to believe that need blind really meant they didn’t look at it, but after the revelations from the Harvard lawsuit apparently they do. For the non need blind schools they certainly consider it.

“My end goal is to be accepted to the most elite business school possible”

Shouldn’t the end goal be to enroll at the school which is the best fit rather than merely chasing prestige? Do you know the area in business in which you want to concentrate. If technical, maybe MIT or Georgia Tech are for you. If entrepreneurship, maybe Babson. For investment banking, maybe Wharton or Stern.

If you are merely after prestige, take out the rankings guide and apply to Indiana among others. It’s a top school and Kelley has automatic admission if you have 3.9 (can be weighted) and a 1390 superscored SAT.

They can assume you’ll be full pay if you don’t submit a financial aid application.

Relatively few colleges are need-sensitive (/ “need-aware”) for U.S. citizens.
(https://en.wikipedia.org/wiki/Need-blind_admission)
You can assume that high need may have a negative impact on borderline applications to those colleges.
That doesn’t necessarily mean you can safely assume that being full pay will have a significant positive impact on applications to those or any other colleges.