I think, for USA at least, you're conflating "city of" with "CSA" and "MSA". For example, most larger cities have what's referred as a "greater metropolitan area" or "metropolitan statistical area", but the whole area, particularly to non-natives, is referred as "Los Angeles" or "Chicago" or "Houston" or "Philadelphia", which are actually a number of smaller, outlying cities/towns. These fall into a third category of city structure, "metropolis". A guy from Arlington Heights, Illinois passes into Bowlingbrook Illinois, and he knows these are two municipalities, but a guy from Germany pretty much sees, and calls, the whole thing as "Chicago".
Yes, because those SAs define the actual urban areas. I'm familiar with the existence of multiple municipalities, I just don't see why they're any more relevant than in London (which has about 30 municipal governments) or Sydney (which has like 30 or 40, depending on where the mergers are at now). The guy in Berlin knows he is in Neuköln or Spandau burrough, with an elected council in each case, but he's still in Berlin.
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