The top-20 schools have the pick of the litter, they can choose whomever they like from applicants all over the world. That leaves all other schools to choose from a thoroughly picked-over pile.

As a university teacher the most important thing you have to do is to pitch the level right. Anything that isn't a top-level school suffers from the tyranny of low expectations, and the cliff after the first 20-25 schools in the rankings is really quite steep. There are no public ivies.