Life comes quick and hard. Usually it is generally pretty easy, but at those times we are not good at getting those people the help they need in time. I really think as much a pain in the butt politically we find all the instant communication technologies and ability to use A.I. to find patterns, this is one area it can really help a lot. It would not be hard to set up a system to give people several options throughout the country, from place they could move into, job they would have, schools for their kids, transportation, and get them on their way when they decide the right one for them.
I think it is still easier and benefits society more to just pay for them to have what they need and help their children to become productive members of society. Make sure the kids have food/clothes/as safe a place to sleep as possible with their family.
Basically that is what Reagan shut down all of the mental hospitals (not that I don't have deep concerns about a institution that prior would lock up and abuse women) Carter got built to pay for his Wealthy White Heterosexual Male Only bases tax cut. Is there studies of how to best house these folks, they would need centralized care I would think, at least resources, we have to have better ideas than just locking people up at this point.
I think the blame is misplaced. I don't think they can be lumped together, and aside from the normal % that seems to be serial killer capable, none of them are out to get anyone. I think the majority of them were born into it and have never had any reason to think about how to best spend the money hiring the right people to actually fix a problem to the point they would bother to take the time to learn enough about any issue not to just tweet about it and go back to whatever they were doing in the first place.
The ones that do take the time to tackle something in the world they think they can help, they have to prioritize doing something truly earth changing and how to actually go about doing it vs something they enjoy doing that they think they can help with the resources they can responsibly spend without giving their children less than they were given to them by their parents.