The entire justice system most certainly does not profit from private prisons. Private prisons are an expense, and given the choice we would much rather lower incarceration rates and not send them there in the first place.
I quoted rates for the same crime because that's what's relevant when considering rehabilitation. If a criminal is arrested for violent assault, spends 5 years behind bars, is released but then re-arrested for minor drug crimes or technical parole violations, that doesn't mean he isn't rehabilitated.
Yeah, your information is not only laughably out of date, you fail to realize that REARREST and REINCARCERATION are two completely different statistics. One can be arrested without being incarcerated, and one can be incarcerated without being arrested (this usually for parole violations).
Here's a study from the PA department of corrections, where I am.
http://www.prnewswire.com/news-releases/pennsylvania-department-of-corrections-releases-landmark-state-recidivism-study-193839961.html
The OVERALL recidivism rate is 60%. That means that within three years, 6 in ten are rearrested for some reason. This number sounds bad, until you dig deeper.
Technical parole violations are for things that are NOT illegal, but instead a violation of terms of parole. Entering a bar and drinking, leaving a geographic area, not checking in with a parole officer on time. These go straight to prison without being "arrested." Of those who ARE arrested, 3/4 of those are Part II offenses- and Part II offenses are almost all minor drug crimes.
18 states and the district of columbia have no death penalty. Of those states that do, it's rarely used relative to the amount of prisoners within the system. PA has a death penalty, but hasn't involuntarily executed anyone since the 1970s.
Keep in mind that the PRISON SYSTEM has nothing to do at all with who ends up with the death penalty, that's decided by a jury.