But even ignoring the suffering inflicted by the prison system, both on the incarcerated person and their family, your example should make us ask -- when does it even make sense to put a person in prison to remove the opportunity to do crime?
How much do you think a person takes per mugging? People don't carry that much cash these days -- suppose one mugging gets you $100 (seems high). Apparently the cost of keeping someone in prison varies by a lot from state to state, but an average value is around $33k, which comes out to around ~$630 per week -- i.e. we're likely paying more to keep your hypothetical criminal in prison than they would cause in crime on the outside.
And when you look at stuff like drug crimes, it gets hard to even figure out what the actual cost to society is for the crime -- but we put a lot of people in prison.
Even if you disregard the suffering inflicted by incarceration, even if innocent people are never convicted, sometimes prison is a bad deal for _everyone_.
Also,
> truly rehabilitative is simply impossible
How did you reach that conclusion? Surely such a broad statement deserves some support.
https://www.vera.org/publications/price-of-prisons-2015-stat...