Obviously not all interns are equal. I guess I should have clarified that I meant at companies like Jane Street which have strong internship programs. They have difficult interview processes, pay very well, and interns actually do interesting work.
It's extremely difficult to get an internship at a company like this. These aren't run of the mill interns who are coasting through college and trying to check the internship box.
Many seniors would never be able to do the stuff in the OP.
Sure, go ahead and use quality of school as a filter, but don't go around discriminating against top public schools while accommodating what are honestly fairly mediocre CS programs at certain Ivies / prestige-private-schools.
...as opposed to give every person a fair chance based on merit.
The statement that "talent is evenly distributed across the world, but opportunity is not" is very, very true.