One the main reasons for the street parking bans is that many of our residential streets just aren't wide enough. On our street, if two cars are parked opposite each other on either side of the street, there is barely enough room for a passenger vehicle to get through. Even with one car parked on the side of the street, there isn't enough room for two way traffic. The primary concern from the city's point of view is that overnight street parking, a time when people are most likely to be home with all their extra cars, can make it difficult for emergency response vehicles, city maintenance trucks, and snow plows to get through. This is particularly true on cul-de-sac streets, where there is only one way in and out.
Things may be different in other cities. For example, Pedro mentioned he lives in a neighborhood where houses have no driveways. In his case, the city doesn't have an overnight parking ban because it would leave people in his neighborhood without a place to park. It was the same way when I lived in Chicago, but there the city required you to buy a parking permit to park on the street in certain neighborhoods. And of course there was the unwritten rule that you could put tables and chairs in your spot to save it when you dig yourself out after a snow storm.