In short, like many laws on the books today, a ban on violent felons possessing a handgun gives the legal system leverage when they are arrested, for whatever reason.. be it being picked up dealing drugs, or in the process of an assault, or after the fact.. If they are caught with a gun, it's one more charge in the court system that can be used to leverage a plea deal and put them away without a lengthy and costly court trial procedure.

You could argue that doing this leads to the imprisonment of the not guilty individuals who can't afford decent representation, but I also blame that on the overall structure of our legal system today, among other things.