>[1] Even worse: While I agree with premise that we should strive for a better educated electorate, someone arguing the opposite could easily point out that the increasing political discord is correlated with the increasing fraction of degree holders.

Hitler had extreme disdain for academics. It's definitively a driving for polarization since it's so easy to draw the line. People who drop out/never enroll have a lot in common with each other and people who graduate have a lot in common with each other but once you compare college educated and high school educated people the overlap starts shrinking.