You make it sound as if that trivializes the process. But I agree that there's something to be written there. It sometimes seems to me that democratic processes around the world struggle (or fail) to scale to the number of people represented. Maybe 300k is just a good size for many of the decisions made by a legislature.
On an unrelated note, Athens during the golden age hat around 300k inhabitants. Of course, nearly half of them were slaves, and less than 10% of them got to vote.
It'd be worth rating the democratic quality of various cities and comparing their populations. The US has good number of cities that fall on both sides of that line. The results would be muddied by county/state/federal influence, obviously, but it'd be able to be suggestive.
On an unrelated note, Athens during the golden age hat around 300k inhabitants. Of course, nearly half of them were slaves, and less than 10% of them got to vote.