Public safety: pre-meditated murder, aggravated assault with a deadly weapon, sexual assault and sexual battery, rapists (non-exhaustive list)
Mental state: think psychopaths where there is no potential for mental rehabilitation (also could fall under public safety, but whichever is fine)
Benefit to society: child abusers, domestic abusers, pedophiles, anti-vaxxers (joking (kind of))
I will stipulate to your statement that we don’t need prisons to separate citizens from society if you stipulate that as of 1/16/2019, there has not been demonstrated a better method in the United States. I’m all for prison reform as I’ve said, but due to a plethora of reasons (a large one being we already suck at putting people into prison when it’s the only option let alone one of many options), we should work to improve what we have already in place. Fix the problem we are currently having with prison infrastructure (literally and metaphorically) before trying to reinvent the wheel on it.