> other than our sense of justice and desire to punish someone for doing something bad, what is prison supposed to achieve?
To keep a person from doing something harmful again when we don't know any other way to make them not do it and we aren't willing to risk more harm.
Sure, if we could magically change the person so they would see what they did before as bad and never do it again, we wouldn't have to keep them in prison. But we don't have any way of doing that. What techniques we do have for "rehabilitating" people are simply not very reliable, so there's a limit to how much we are willing to depend on them as an alternative to incarceration.
Except you're missing the point that other countries have less-horrible prisons and programs to keep inmates somewhat connected with other human beings and better prepare them to resume a normal life after their sentence.
It doesn't matter that we can't see the future when we can look at the present in other locations and see better results. We do know another way - the US prison system is just blind to it.
To keep a person from doing something harmful again when we don't know any other way to make them not do it and we aren't willing to risk more harm.
Sure, if we could magically change the person so they would see what they did before as bad and never do it again, we wouldn't have to keep them in prison. But we don't have any way of doing that. What techniques we do have for "rehabilitating" people are simply not very reliable, so there's a limit to how much we are willing to depend on them as an alternative to incarceration.