The problem with prison labor, and privatized prisons, is that they introduce other incentives to the whole equation- profit & graft.
When prisons show a profit, there are no disincentives to extremely long sentences for relatively minor crimes, because they'll make money off your junkie ass every day you're locked up, and they have ways to convince you that picking cotton all day out in the sun & living in a tent w/o running water for 30 years is preferable to the alternative.
That's the way many bible belt prison systems worked for decades, and the rake-off, the graft on the part of prison guards & officials was incredible, yet not enough to prevent them from putting money back into the general fund every year.
The more people you lock up, the more money you make. It's a state sponsored form of slavery rather than the necessary incarceration of criminals. We need to have to pay to lock people up, just to keep the system semi-honest.
Having known several ex-offenders, I believe that inmates generally regard work details as a welcome break from the drudgery of prison life, particularly any that get them outside the facility. More of it? OK, just not enough to significantly reduce the cost of locking people up, and especially not enough to show a profit.
Privatized prisons are an abomination from start to finish, perhaps one of the most sordid panders to corporate interests ever invented.