Differing county education funding was a real and evident problem when I was growing up in Massachuesettes in the 90s - some areas (like Wellesley) had extremely well funded schools due to local taxes while other areas had far too many students for the funds they collected. This, in part, lead to a whole big thing involving student busing[1] which was honestly pretty awful for the students that rode several hours to attend suburban schools - even if they did end up in a better funded district it was a cheap patch that avoided the real issue.
1. https://www.theatlantic.com/education/archive/2019/04/boston...
Lots of land is outside of cities, and that can't be left ungoverned. And many counties have very few people, which make a lot of government functions impractical or insufficient.
So states are still a reasonable unit after 250 years.
I don't think going by names is the best approach when we've got legal documents and statements to go by which are far less vague.
This makes sense because we want people to freely move around the country without encountering wildly different systems in every small town.