It's amazing how twisted adult mindsets about sports are. Notice how not caring about watching pro sports teams is, in your mind, "not liking sports." As if the primary function of "sports" is to be watched, rather than, y'know, played.
> It is a marker of quality for a city, a stamp of approval.
I really don't think so. It's more likely that causation works the other way: cities that are successful tend to attract sports teams to take advantage of the local market.
Take Seattle: lost its NBA team, lost its NHL team until very recently. Was just found to be the most desirable city for new college grads anyway. Nobody's been thinking that Seattle sucks because they only had two of the four major US pro sports present in the region.