That cost should be taken by our government and the tax payer, as a disincentive to locking people up.
If you can lock someone up and get close to free labor for it, then we're going to start locking a lot of people up. I mean, it's free labor. Which is why we used to give people 20 years for possession of marijuana. What, you think it's just a coincidence we were throwing primarily black Americans away in prison for ludicrous amounts of time where they'll spend their days picking cotton?
That's what happens when imprisoning people is cheap.