I think building a whole city as a prison wouldn't work, because it would have the same problems as a normal prison.
Putting a bunch of criminals together in one place doesn't make them change their way of life. Most of the smaller kind of criminals end up even deeper in the criminal scene when they are released from prison.
I don't think that ,with a crimefighting-organisation like Batman-Inc. already being built up, Batman would let this happen in the regular Batman-Continuity.
Although i think that this is a really interresting story for a game.