They could be paid for their work. It is labor, after all. And they don't get a choice.
The removal of their liberty is supposed to be punishment for their crime, and that's plenty of punishment. Ideally, they'd be reformed while in prison. And while I'm dreaming, they could build a nest egg by working there, instead of being exploited.
What would have happened had they refused to work? They won't get whipped or beaten.
Arguably community service under threat of imprisonment is also compelled labour. If you agree that's a valid punishment for a crime, then we're not really talking about whether compelled labour is a problem in and of itself so much as the specific conditions under which labour can be legitimately compelled.
I can appreciate the desire to ensure criminals have some money when they get out since a lot of crime is correlated with poverty and job prospects are slim. However, you're neglecting that prosecuting and incarcerating people costs society money, which is to say that criminals owe society a debt, and in principle, criminals should be paying as much of that debt as is feasible.
That said there are multiple ways to do this. One is compelled labour the proceeds of which they'll never see, but perhaps work can go to lowering their sentence. Another can be deferred compensation, where they get a fixed stipend once out based on their work while incarcerated.
I can think of a bunch of other ways, but I'm not sure I agree that the compensation should be minimum wage. People fund the government via taxes, but criminals aren't just not paying into the system, they are actively draining it. I'm not sure garnishing wages they'd otherwise earn is in principle unjust anymore that income tax is unjust.
This does ignore the damage done to the free market though. Every job that a prison inmate takes up, is a job that could be taken by a non-criminal and which would pay for at least federal minimum wage.
I'd call the difference of prison wage and the minimum wage lost money.
I agree there are externalities to consider for a proper proposal, my purpose here was only to argue that compelled labour without minimum wage compensation isn't intrinsically wrong, it depends on the specific implementation.
The removal of their liberty is supposed to be punishment for their crime, and that's plenty of punishment. Ideally, they'd be reformed while in prison. And while I'm dreaming, they could build a nest egg by working there, instead of being exploited.
I'd like a pony, please.