While I agree that the US has a serious imprisonment problem (jailing people for the wrong reasons), I have to believe that getting doctors to work in the prison system requires some significant financial incentives -- and most of these people seem to be medical professionals.
The average cost per inmate in California is about $49,000, twice the cost to run prisons in other states (the average is around $28,000). Some states are even less. The average cost per inmate in Florida is under $20,000. Texas is a little over $15,000.