A third possibility is 'removal'. The idea is that a potential criminal is under the control of the state.
Correlation vs. causation and all that, but given the likely lack of results from either punishment or rehabilitation, perhaps that is what happened here.
https://marroninstitute.nyu.edu/uploads/content/_1400_700/Cr...
The problem with this approach is that its counterproductive, as many prisons act as graduate schools in crime.
Combine this with society mandating severely curtailed opportunities to participate in non-criminal work and you get a perfect storm where prisons churn out more hardened criminals, which leads to more crime, which leads to more prisoners.
As are the streets.
In this model of 'removal', I'd say that the main point of a prison is to take a more crime prone demographic (by that I mean age, gender, ethnicity, location, wealth...the whole ball of wax) off the street until they are older and less likely to do things that the straights don't like.
In the long run, I would expect for universal surveillance (and the increased ability to parse data we are seeing) to be the main driving force in social control rather than mere warehousing.
If I were designing a prison system, it would be a mini-society. Only a minimal set of rules would be specified and enforced by those outside the prison. The rest would be voted on and enforced by the prisoners themselves.
I don't think I'd recommend it for the U.S.