All those definitions use “city”. Does the definition of city require the kind of density that would make relying mostly on self-owned cars impossible? Depends, in america no, in other countries maybe.
No. “City” is a legal designation for an inhabited area. Some legal frameworks place a minimum population requirement for designation as a city but none (AFAIK) require a population density value.
For example, Oklahoma City is the largest city in the US by land area (or it was a few years ago) because the city limits were drawn that way. Population density was and is very low but it’s still a city.
Does the definition of city require the kind of density that would make relying mostly on self-owned cars impossible?
Ooooo, self-moving goalposts, nice!