The geometry argument was not as simple as you suggest.

There was a necessary precondition: "there's ultimately a limit to how effective personal cars can be when population density exceeds a certain level".

That's the opposite of implying that one form of transportation works best everywhere.

FWIW, in some low density areas the most successful form of public transit is the ferry, which carries kids to school, people to work, food to the stores, and more.