Well, it's a very important part of the feel of a place. Life in say, Kennebunkport is very different from life in New York City. The pace is different, the goods and services available are different, the size of the city government is different, and all of these things affect gameplay in a fantasy city. For example, I can easily accept that the Red Dragon would be the only inn in even a large city that adventurers would note and seek out, but just how much does it dominate city life for the locals? Can you step outside and either be outside the city gates or at the opposite side of the city in 5 minutes? Or does it take an hour of walking just to get to the nearest gate?
Getting that feel right is an important part of creating a persistant, believable world. In a small city, there will be a handful of prominent local NPC's that pop up over and over again. EVERYONE will go to "Bob the Armorer's Shop" and "Jim's House of Magic Supply" because Bob and Jim are the only two guys in town who sell that sort of thing...it makes sense to create Bob and Jim as NPC's, and to create a little background and personality for them.
But in a very large city, there'll be a whole street full of armorers, and another street full of weaponsmiths, and at least 3 or 4 places to get magic supplies. Instead of, "You go to Jim's, and Jim recognizes you from the last time", it's "You go to Magic Alley, and after a half hour of shopping, you find that one of the merchants will sell you a Quasit's tail for 75 GP." The "magic merchant" can be nameless and faceless, because there's no compelling reason for a particular character to ever see him again, as the PC will just as likely do business with a different merchant the next time. It's that "look and feel" thing again.
Also, bounding the city size bounds the size of the city map, and quite possibly bounds the amount of detail that you want to put in the map. It makes sense to mark every tree, hitching post and outhouse in a small hamlet. In a really huge city, everything gets abstracted to laying out large districts, noting the most important streets, and highlighting a few points of interest...there's neither need nor time to lay out thousands of houses, shops, taverns, temples, etc.