It's a nice idea, but I'm not sure the statistics line up. Searching online gives the proportion of the population (age 25+) holding at least a bachelor's degree in the USA to be around 50%, which is higher than in Switzerland, Denmark and the Netherlands, to make an arbitrary selection. In fact there is no northern European country whose population has a higher proportion of tertiary education attainment than the USA. As far as I'm aware, primary and secondary education is available without cost in both the USA and across the entirety of Europe.

Percentages aren't of course the whole story; maybe secondary education in these countries is of such higher quality that fewer people need to study further to participate intelligently in political discourse. Perhaps the implications of free degree education on graduates' personal finances gives northern Europeans more free time to use that knowledge and participate in politics.

I like the idea of free education, but I am not confident that this is to blame for the USA's issues - mostly because of the situation in my country, the United Kingdom. Despite having had no tuition fees until 1998, this has not done anything to prevent an almost completely two-party system from prevailing for the last hundred years. For me, the non-proportional electoral system has become both the probable symptom and the probable cause of voting tribalism in both countries.

Ah that's a good counterexample. Political education could play a big part, as well as independent media.