I'm certainly not a constitutional lawyer, so I ask out of curiosity: has the 13th amendment been interpreted this way?
I feel that there's a difference between slavery as punishment (i.e. being explicitly sentenced to slavery) vs. slavery incidental to punishment (i.e. being explicitly sentenced to imprisonment, and then the private prison deciding to enslave you during your sentence).
That is true about unpaid labour, but my understanding was that this isn't forced on to the prisoners. I understand that prisoners are given the option to work, and reap various benefits in return (modest pay, extra hours outdoors in the case of road crews, and potentially leniancy for "good behavior" at parole hearings).
I feel that there's a difference between slavery as punishment (i.e. being explicitly sentenced to slavery) vs. slavery incidental to punishment (i.e. being explicitly sentenced to imprisonment, and then the private prison deciding to enslave you during your sentence).