That problem lies in the assumed nature of justice. The USA is deeply wedded to a system of retributive incarceration; the purpose of its prison system is to punish those convicted of crimes. This leads to many problems. First, those convicted are tainted by their history of having been incarcerated; it's received wisdom that all a person learns in prison is how to be a better criminal. This perceived untrustworthiness follows the person for the rest of their life, restricting their opportunities to make a living honestly. Eventually, inevitably, this leads to the thought of "if I'm going to be accused of this, I might as well do it", creating a cycle leading to mass incarceration.
The desire to punish is rooted in a view of people who commit crimes as intrinsically criminal. In reality, the most common cause of crime is despair; the criminal life is not easy, and people will generally take the easiest path open to them. If we truly wish to reduce crime, we must reduce societal inequalities, act to alleviate poverty, and ensure that everyone has ample opportunity to improve their life. Education should be treated as a necessity, not a luxury.
Whither prisons? If we adopt the view that those committing crimes are doing so because they see no other viable means to survive, then we must show them legal means to survive. Prisons should provide career advice, education, opportunities for personal enrichment through art; treat those incarcerated as people who need help, not as evil people who need to be punished.
We must also work to destroy the current stigma imposed by incarceration. In the USA of 2016, anyone who has been to prison is effectively barred from employment as anything more than a menial labourer.