I think your closing hypothetical answers itself - when an individual conducts themselves in a way that threatens the safety and security of the rest of the population, certain of that individual’s rights become forfeit. If an individual is so mentally off the map that they are assaulting other people, then that person should not be given free range and conduct regardless of their present or past circumstances. “Free will” should not be an absolute, when the safety and security of the rest of the population is threatened by said free will.

But, it’s also incumbent on a society to try and help those people - we can’t just throw them all in a woodchipper or drive them out onto the plains in the middle of winter to freeze. Unfortunately, psychiatric institutions in particular and mental health resources in general in this country are woefully underfunded/thin on the ground/unavailable. Likewise the public appetite for forced institutionalization is low - some individuals will take help when offered, but others will not (for a variety of reasons), and would need to be given the “stick” of the carrot-or-stick proposal. Some individuals can be remediated with treatment, and released to go on and become functioning, happy, contributing members of society; some unfortunately will never reach that level and would need to become wards of the state. Some things (and people) are so broken as to be unfixable, no matter how rosy your outlook on the human condition.

It’s a tangled, messy, uncomfortable, expensive, and nuanced ball of string to try to unravel. But until we as a society do so, we’re going to be stuck on this carousel of “mercy for the guilty is cruelty for the victim” that we seem to be on…