If you look it up, there was actually a professor at UCLA who found that accepting URM students to better schools actually results in less URM lawyers because students are more likely to be overmatched at their school and drop out (this obviously isn't true of a student who would go to Chicago and instead is going to Yale, but it is true of students in the T3/T4 range).
That said, it isn't all about the students. Schools themselves have an interest in diverse campuses. There's a reason why private schools, who are under no law or obligation to give special status to URM students, continue to do so: it helps their reputation as a school. Race may be a somewhat generic way to promote diversity, but it is one way.