I'm not expecting anyone, but the dragonborn to be taking down dragons on their own, but a single dragon against an entire city guard shouldn't be able to raze the city. If your swords/bow/magic is hurting a dragon, then it shouldn't be immune to anyone else's swords/bows/magic.
I agree that a collection of tougher NPC's should be able to at least drive off, if not outright kill, a dragon. However, by "should", I mean from a game mechanics perspective, not necessarily a logical one. After all, Bethesda could say that dragons are effectively immortal and indestructible, and it's the shout of a Dovahkiin specifically that makes them vulnerable to attack. In that respect, the "if my sword can cut them, anyone's can" argument goes right out the window. However, I don't think that's wise from a metagame view, since (as others have pointed out) the PC can't be everywhere at once, and a crew of a few dragons could then quickly decimate towns and murder all inhabitants of the world.
Maybe it's something in between though. Perhaps the shouts do make the dragons more vulnerable, which is why the PC has a shot when taking one on by himself. A collection of NPC's can bring one down, but they're much heartier and difficult to injure without being affected by a shout first.
Just pullin' at straws here, but I think that makes sense from both the game mechanics and lore sides of the fence.