Believe it or not, a huge number of incarcerated people would rather work (without pay) than sit around doing nothing. For the few that don't, you can certainly incentivize it without resorting to torture.
And in fact, one of the common punishments available to prison staff is to bar the prisoner from working if they are getting in fights, etc.
The prisoners wouldn’t mind working for more pay, but most of them do like it considering the options.
Another part is just accounting - if the federal government paid its employees tax free (no fed income tax) it would work out the same (salaries would drop) but the accounting would be different and people would complain.
But why not pay them? Perhaps you cannot pay market wages without a being a competitive capitalist enterprise, but surely there is a point where access to subsidized labor allows you to break even, paying them, say $3 or $5 an hour.
And perhaps you cannot pay them in cash, but why not invest the money for the duration of their incarceration, or pay a stipend to some dependent on the outside, like a wife/child? A $10k/year rate of savings is above what many people achieve outside, and a massive boost to get one's life in order once they get out.
Is it torture when you force kids to do their chores? Surely there are ways. But regardless don’t a lot of inmates volunteer for work? How much is forced?