There is discussion of these partial lotteries in academia as a way to improve the procedure of getting grant money. https://journals.plos.org/plosbiology/article?id=10.1371/jou...
I've always felt it modern democratic politics would benefit greatly from such a system. I'm not sure the same is true of academia, you want students good enough that they do not risk failing at an elite institution, but when setting the threshold for "good enough" it's easy to reproduce the same inequalities you were trying to avoid in the first place.