I think you grossly overestimate the percentage of candidates at lower tier schools who would be qualified to pass a Jane Street (or really any HFT firm) interview. Even at the top schools the pass rate is incredibly low. In expectation you would be getting probably <5% of your new graduate/intern class from the entire bottom 80% of schools.

The quality level drops off very sharply after you go below the top 20-30 CS schools. It's just a matter of limited resources for recruiting. The common path taken by people who go to "lesser" schools is to grind really hard to get into a good MS or PhD program and then go to these firms.