This assumes that incarceration rates should be equal for all races, which probably shouldn't be the case. There's a correlation between low socioeconomic status and incarceration. Black Americans tend to have a lower socioeconomic status. Murder rates are also much higher among blacks than other races in America.
> Prisoners are, by design, excluded from minimum wage laws.
Right. Prisoners are being exploited, but that's not why they're being imprisoned. They're being imprisoned because of drugs, violence, and thievery/burglary for the most part.
Yet the theory breaks down once you look at a breakdown of race, gender, and SES.
There's plenty of research debunking this claim, which is a myth generally propagated by groups with explicit white supremacist agendas.
Nobody is saying "only" black people are being incarcerated. They're saying that incarceration is used as a tool to perpetuate many of the same outcomes as slavery. Which is trivially verifiable, if you look at the respective incarceration rates by race.
> they're being incarcerated explicitly for cheap labor
Virtually all prisoners are required to work for what amounts to as little as $.10/hour. $1/hour is considered an incredibly good wage for a prison job. Prisoners are, by design, excluded from minimum wage laws. This is not limited to private prisons; it includes inmates at state-run and federal prisons too.
In California, about a third of the people fighting the recent and ongoing wildfires are prisoners, generally making about $1/hour or less. The maximum they can make is $2.56. Again, this burden largely falls on black and other non-white people, because they're incarcerated at much higher rates and for much longer sentences for the same crimes.