While I agree that preventative measures help to reduce crime, it will not stop it. That is why we have rehabilitation, so that the people who do commit crimes do not commit them again.
It's not about preventative measures. It's about solving the problems inherent and ingrained in society, specifically class, race, and gender among others of course, that are the cause of these problems.
Many have previously argued (not necessarily in this thread, but in general), that Europe's prison systems are superior because they are more accommodating to the prisoner and treats them respectably, which falls in line with the rehabilitation theory. And I'd agree that the prison environment, especially in state, local, and private prisons needs to be changed as it breeds more criminals, but that isn't the end of what needs to change. When you leave a prison in Europe, you're probably going back to an okay standard of living with free health care and other social benefits. You're probably not in a constant struggle for survival. However, here, while the poor may be some of the richest poor in the world, that doesn't get them shit in the way of reasonable accommodations to live OR social mobility. If you have a crime like robbery or drug trafficking on your record, no matter what your circumstances were or what society has done to get you to that place, good luck getting a job. If you have a felony, you might as well forget about trying to get a good job. You might be able to get a pretty shitty job if you have a lesser crime on your record, but minimum wage is not enough to survive on.
So what's the result? Back to crime. Sure, some commit crime because they are mentally ill, and it is much more clear so, and they should definitely be the focus of rehabilitation, even if it is mostly a failure, but I'd argue that most crimes have causes that are rooted in the way our country and society functions, which is more of a sociological perspective on the issue.