A publicly owned and run prison service would be continually seeking to reduce cost
Even when government run, it is desirable that prisons do "business". I.e. make the prisoners do some work, and earn their food , shelter and even incarceration. Reasons :
1. Keeps motivation for capital punishment down. So that public doesn't scream why should this murderer be kept alive on my money?
2. In doing nothing at all, prisoners will be unable to cope up with post-release life. Prison - management is not enough work - cooking, cleaning, prison stuff repair doesn't add up to enough work to keep all prisoners busy.
3. It's simply good money-management. There are people who can't be freed, need to be made to work, and need to be fed. Rather than giving them money to dig pits and fill them back, make them work which can be sold for money.
So there is not just the reduce cost dynamic going on here, but also increase income. Also the fact that government itself doing business is a taboo in the US.