The punishment is being locked up in a cell. Being forced to work on top of that is the slavery.
Why is it not part of the punishment?
I think it is dependent upon interpretation. Otherwise arresting and locking up can be interpreted as kidnapping and so on.
I do agree that they should be fairly compensated though.
Indeed it is part of the punishment. As an earlier comment in this thread points out from the 13th amendment:
> "Neither slavery nor involuntary servitude, except as a punishment for crime" (emphasis added by me)
They're not. That's why it's slavery. And slavery of prisoners is permitted by the Constitution, which is the main point here.
Why is it not part of the punishment?
I think it is dependent upon interpretation. Otherwise arresting and locking up can be interpreted as kidnapping and so on.
I do agree that they should be fairly compensated though.