While I agree with your remedies for the re-incarceration (I can't remember the term) rate, the reason we have so many prisoners is quite clear and if anyone does a little reading on the subject will come to the same conclusion.
We have 5 times the prison population of Great Britain, 7 times that of France and 12 times that of India (I bet India's jails sucks more than ours). Looking at the numbers per capita they get even worse, you can pursue them on Wiki if you care to.
Our prison population remained rather steady up until the 1980's. From the mid 80's to now the prison population exploded from roughly 300K to more than 2 million. Now we know when the problem started, what happened in the mid 80's that caused this explosion in prisoners? The anti-drug-abuse act happened and it caused two issues. One was the increased prosecution of non-violent and mostly non-threats to society and it implemented draconian mandatory minimum sentencing. People like to blame the increasing privatization of prisons but that is just one of the symptoms of the disease. Police departments get more funding, including federal funds and property, the more arrests they make and arresting poor people for low level drug offenses is the "low hanging fruit". Seizure laws added jet fuel to the already growing fire. Then still riding on the "tough on crime" push in the 90's states started passing 3 strike rules so a guy caught 3 times with an ounce of weed was mandated by law to get a minimum of 25 years in prison. Local governments have increasingly used the justice system as a major source of funding, some even their primary source of funding, creating debtors prisons. Federal prisons are no better, half of all prisoners in federal prison are there for non-violent drug offenses.
Fun fact: 1 in 32 Americans are currently incarcerated, on probation or on parole. That is just insane and proves that our system is seriously broken.