This is problematic in many ways.
First, it hinders anyone trying to move units into the city's surroundings to protect it from any resistance left. This is especially true on later eras amphibious assaults, where the captured city can act as a port and allow any embarked unit to retain some movement points upon disembarking.
Second, we may also have plans on what to do with the city immediately after capture, like moving its great works to other cities, using an inquisitor and moving air units to it (especially with Imperialism's finisher).
Third, I sometimes am sieging two or more cities at once and can capture two in the same turn. I see no reason why one division capturing Berlin should prevent the other from liberating that formerly allied city-state that Bismarck annexed.
Fourth, it could lead to another cheesy tactic in which one city could be kept from being conquered by having another flipping sides.
There are other things, like how it would work if you have other mandatory things to do, like voting on the World Congress, or if you planned to peace out immediately after capturing the city. Overall, I think this proposal is problematic.
That means any unit garrisoned in it gets blapped by any attacker due to the city having 5-11

CS. A riflemen attacking it would deal 300 damage going straight to the garrisoned unit. It's already tough as it is, but the city's recovered health allows for the garrison to live a bit.