With what we do in the US, it’s not “punishment”, it’s sadism. Justice ends when excessive punishment begins and is deep into sadism when torture begins.
I'm sure most people would want that, but I don't think that we know how to "make people" change. Much in the same way that we don't know how to have school "make children" more academic, we don't know how to make inmates less violent / impulsive / thrill-seeking (except by the inexorable passing of time). I'd be very happy to be corrected, tho.
OTOH, giving proper (i.e. often involuntary) treatment for violent mental illnesses would for sure improve the situation.