Our system isn't vengeance based, it's based on consequences of actions in accordance to the law...or it is supposed to be. It is far too soft, to be honest, between corrupt officials and bleeding heart crybabies who clamor and insist that all criminals are victims or misunderstood or some crap. Sadly, it's broken because there's too many easy-outs and shortcuts, and not enough funds to do things right. There's other problems too, such as persecution of some criminals doing things that in of themselves should be decriminalized (take pot smoking; if nothing else, I think that should be decriminalized for users who aren't endangering others simply to clear out room in our prisons for actual dangerous perpetrators and to lessen our tax dollar burden and the stress on the judicial system as a whole).
But back to your accusations of thinking you know what I believe, my ideal system wouldn't be more akin to none of them should have contact with one another except during 1 hour of exercise a day (no weights; running or walking only). Smaller cells and solitary confinement for all of them. The only other time they might see others would be on work detail. Longer sentences, too; early parole should be abolished. The point is, I don't want to watch; I want to keep these vile wretches away from law-abiding citizens for as long as possible. Choices have consequences. We shouldn't have to rehabilitate those who are either too stupid or didn't care enough to act as they are supposed to in the first place. Juveniles I can understand; rehabilitate (or try to) away. But I expect more out of grown men and women.
And again, your system is what the prison system was in the past and still is. it doesn't deter and doesn't fix the problem.
Look to the countries who's actually fixing the problem.