That gets extremely complicated. My town straddles the border between 2 counties. And you can't trivially have subdomains for counties and cities at the same level, because Wyoming has a Laramie city but it's in Albany County, not the neighboring Laramie County.

Did this just inspire the next "Falsehoods programmers believe about... Federalism"?

Virginia cities are independent, not within counties. And there's both a Fairfax City and Fairfax County. Making things even more confusing, the county seat is Fairfax City despite the city not being part of the county. The county has fairfaxcounty.gov while the city has fairfaxva.gov.

There are a handful of other independent cities in the US, but the vast majority are in Virginia.