Bingo
A little more expensive than your posted proposal, but with the same outcome.
It is where those men belong, and it is what must happen to them.
The problem is: what are you going to do with the guards? Extermination of their prisoner population will change the guards, and many will have a very difficult time returning to a relatively peaceful society their work may have created.
At some point they will have culled the five percent of the population which is responsible for the violent crime problem. Then what should they do with the mostly empty prisons? Should they expand the ranks of eligible persons to be sent there or should they close them down?
I hope they have plans for the results of the program success.