The State should not force the prisoners to work, but it also shouldn’t be the State’s responsibility to provide janitors or cooks to look after them.

You should understand that this represents a logistical problem for the prison. Now they have to ensure that prisoners are certified and trained to handle food, no small feat, and you also have to be conscious of the idea that prisoners could pretty easily stop doing dishes, making food, eating food, as a form of hunger strike, in order to protest the very fact that they're being made to make food, on top of the fact that they're being extricated from society, deprived of the right to be a productive member of society, deprived of the ability to socialize with other people that aren't criminals, deprived of free access to information, really, any freedom whatsoever.

That's along with the argument the other commenter brought up, about prisoners just organizing themselves into a de-facto government where the most shat on prisoners will have to do everything. If you decide to come up with a constant rotation, a chore wheel, then at a certain level this just devolves into massive levels of prison corruption, where a couple bribes to a couple prisoner guards can change around some labor forms and then suddenly, again, the most shat upon prisoners are doing all the labor.

You don't eliminate these inefficiencies at any point, either, these inefficiencies rear their heads more the more people you arrest and put into the prison, the more things you criminalize, the higher the recidivism rates. None of these issues resolve magically, they get worse.

This is effectively just the same as advocating for the status quo as it currently exists, with the only minor difference between, say, making license plates or fighting fires, being that instead, they're just doing domestic labor which is much closer to them in proximity, and easier for you to think of as their personal responsibility to handle. That doesn't matter so much, what matters in reality here are the numbers.

The idea is that you're trying to recoup the costs immediately through something like a labor camp, which is what this still is. That's sort of an option of last resort, or an option that is used, in most circumstances, as it is right now, for members of political opposition or other kinds of outright status-quo threats. You instead should make the calculation in the broad strokes, years down the line. Can these murderers, thieves, and perhaps even, gasp, loiterers, be taught to be functioning members of society? Can they give back more than they have taken from the taxpayer over the course of their life? More than just for the individuals, but can these prisoners do this on the whole?

That's the way you should be thinking about this, not "Can we save 15 bucks here and there by not paying someone to clean up or cook for the prisoners?". By framing it like that, you've bought into the argument that supports the status quo organization, here.