URM applicants with even moderately impressive numbers are eligible for tons of financial aid, as well as admission to schools that non-URM applicants with similar numbers can only dream about. Most law schools will bend over backwards to attract qualified URM students with significant scholarship offers. Many of the people who receive those scholarships aren't exactly poor either, but qualify based purely on URM status.
Merit scholarships are different. They are available to anyone, regardless of race, as long as they have the numbers. I think you're probably right that many of the recipients of merit scholarships are from well-off backgrounds, but plenty of regular joes benefit from these scholarships too. And yes, attracting highly qualified students is a legitimate goal of any law school.
I was raised poor as hell by a single mother, and never had any educational advantages. I went to crummy, gang infested schools where nobody cared, and had to work at crappy jobs and go into debt to get through college. Because I'm white I couldn't qualify for AA or many scholarships even though I was poorer than many of the URM students at my college. (Poor white students get really screwed this way.)
The only way I was able to attend law school was because I scored well on the LSAT and obtained a merit scholarship. Even then, I had to attend a lower ranked school in order to maximize the scholarship opportunities.
My point is that it's not as simple as you'd like to believe, and it certainly isn't "racial exploitation". If you don't have the numbers to merit a scholarship and you're afraid of accruing debt, then drop out. No one forces you to go to law school.