The NY Times Magazine outlines the tradeoffs that make it difficult for college admissions departments to admit deserving students and pay the bills: the high costs of college and the link between income and test scores. Indeed when Trinity made standardized testing optional, it fell six places in the rankings.
But I think the article may have missed a bigger issue: the intensifying competition among colleges for students driven individualized pricing, i.e., price discrimination. If you set a single price, competition is limited to consumers whose reservation values are near the price. But when you offer individualized pricing, which is a by-product of financial aid, you start competing for every single student. In essence you turn relatively mild price competition into an auction--for every single consumer!
See Cooper et al. (2007), Does price discrimination intensify competition? Antitrust Law Journal, (also available on SSRN).
If colleges could figure out how to quit offering individualized financial aid--without colluding to do so--I suspect it would soften competition to the point where they could stop losing money.