Maybe not now, but if you actually work on fixing broken people, you'd end up with a prison profile more like Norway's. That wouldn't happen overnight, naturally. The system we have now has resulted in an awful lot of broken people, and they just propagate their disorders to their children. Look at violent criminals now and in most cases I think you'll find someone who would not have been violent if they'd received help at an earlier stage of their lives. People don't become criminals for no reason. Someone doesn't just wake up one day and think "What a nice day, I think I'll go out and murder a bunch of people!" We always know about those people in advance.
Of course, my Socialist-Totaltarian regime has a multi-pronged approach to addressing this:
1. All children will be confiscated from their parents and birth and raised in sanitary state-run facilities. Processes will be put in place to insure that no violent or sexual abuse of the children will be possible.
2. All children will be reversibly sterilized at puberty. Anyone wishing to breed will be required to pass a parental competency test.
3. For anyone unable to pass a parental competency test, the state will choose a partner based on specially-designed algorithms designed to insure the happiness of the couple.
4. All religion will be illegal except for the state-run one, which will involve Smurfs. Non-Smurfy behavior will be dealt with harshly.
I predict that my society would reach the "Utopia" stage within three generations.