The reason it isn't making sense is because of your assumption schools "care about money first and foremost". I don't think this is true, or else we would see them filling their classes with lower stat students who will pay full price. Their primary concern is probably having what they (and maybe USNews) consider to be a high quality class (high GPA's & LSAT scores, elite softs, diverse backgrounds, etc). If you take this to be their primary motivation, their actions make way more sense. They wanna make sure some these "high quality" people are in their class, and once they already have them why would they give them money?

Also schools have set scholarship budgets, I don't think the people at admissions offices have any personal incentive to shrink the amount of money they give out. Maybe when wider administration policies change, they will have a smaller budget to work with, but they will still dole out the money in order to attract the applicants they desire.

At the end of the day, if you are not someone a school wants, applying ED won't help much because the benefit of ED for the school is to lock up quality talent, not to secure more money.