"San Francisco has no right to compare itself to New York. None at all."
Who exactly is the arbiter of this right? San Francisco (and for that matter Paris, Tokyo, Beijing, London, hell even Turlock) are free to compare themselves to whatever other city they like.
Also, you don't need a car in SF if you're not lazy or just coming back from buying a couch, I prefer the weather in SF, and different cities have different good and bad things about them.
As far as capital of the world? Eh... I guess, but London seems the more natural choice for that in many regards.