Obviously you've never actually been on one, nor even know much about them.
While a carrier relys on fighters for a lot, they are never "unarmed" outside of the aircraft.
They actually are extremly well armed, although it's almost all defensive weaponry rather than offensive weapons outside of few missles.
As far as armor, they are as well armored as any capitol ship, which is still pretty much useless against modern weapons. The best you can hope for is to be armored just enough to give your crew a chance to survive long enough to get off the ship before it sinks.
They aren't floating cities, they're floating fortresses.