To note: the entire Switzerland's population is 8.5M, about the size of 5 boroughs of New York City. They have twenty six cantons, all with severely different policies, and 2222 municipalities. Of course most voting occurs at municipal level, then cantonal level.
To my mind, nowhere in the world any larger state managed to get to the "level of democracy" which is possible and has been demonstrably achieved at smaller scales.
What additionally exacerbates the situation in the US is the two-party system that effectively polarizes people instead of nudging them to look for compromises.
The electoral college made sense in 1770s, with a much smaller population, and very slow communication. By now, it results in interesting side effects that probably could be avoided using different mechanisms. Still I think that no large nation has deployed any such mechanisms to successfully achieve "real democracy" and not some form of oligarchy. Mass media is a major factor in that; national scale being hard to comprehend and relate to for a voter is another.