They have an incentive for diversity, but not undergraduate institution diversity.
This is old because they don’t show the numbers anymore, but Yale sends about 25 and Harvard 20 each year out of a class size of 200. (Page 157-159).
http://bulletin.printer.yale.edu/archivepdffiles/Law/Law_2015-2016.pdf
45 of 310 at UCLA are from UCLA.
UChicago accepted 39 of their own students (page8).