We should be providing more of the services I have described - ie community based supportive housing. That would prevent a lot of problems.
Wouldn't have caught Li tho, and I don't think anything we do, short of locking up everybody who acts a bit "weird" would do so. Many people look lost, almost none go on to kill and eat other people.
With Li, and other NCR people, I have no problem with releasing them back into the community if deemed safe to do so, as long as close support and monitoring exists in that community - ie make sure they take their meds every day. If they don't, or otherwise go off the rails, they should be re-institutionalized. Not for punishment because they are responsible, but for the safety of themselves and the community. As for something to lose by going for help, that was not likely his motivation. It's the stigma of being labelled, as well as his internal reality that tells him he's quite sane and how will he stop the aliens if he's locked up.
We do no punish alcoholics for being alcoholics. They are free to drink themselves to death. We punish them because of illegal actions they take that might be driven by their alcoholism. We do deem them rational beings able to make decisions. Which is kind of funny, because when somebody is blotto, they're not rational, not able to make good decisions, so maybe they should all be found NCR for killing somebody too. And in fact we do have the diminished capacity defense for just that. "I was too drunk to form intent, you're honor, so I'm not guilty of murder"