There are many cultural, political, and economic reasons for America's broken justice system, but none are fitting excuses for why it isn't working. The United States has more incarcerated citizens per capita than every other country on the planet, yet boasts one of the highest recidivism rates in the world. People go into prison as petty criminals only to come out as hardened criminals, and you have a private prison industry which incentivizes ever greater levels of mass incarceration (the US prison population has grown by 500% over the last 40 years), often for non-violent crimes, or as a consequence of dodgy plea deals.
The truth is that guys like Baked Alaska aren't going to be rehabilitated by the American prison system. He's a mentally ill man who resorts to unhinged and reckless behavior because he craves the attention it brings him, and he evidently lacks the ability to properly appreciate the consequences his behavior has for himself and others. In a sane world, he'd be involuntarily committed and sent to a psychiatric hospital for treatment; not sent to prison where he'll likely come out even worse.