Then I remember how the definition of mental illness has changed over the years and think how it might change in the future, and now I'm not so sure.
Meaning there are 2 issues
(1) Save everyone else from someone's distruptive behavior
(2) Deal with the person in the best possible way
You can solve (1) and not solve (2). Being not able to solve (2) perfectly does not invalidate the need to solve (1)
1) What sort of behaviors is a community willing to tolerate
2) What does that community do with people who are unable to stay within the confines of tolerated behavior
The problem is that asymmetrical answers to the two questions can create a strange grey-zone, where problems linger.
For example - if you murder someone, I don't think many people are going to argue against you spending some time in prison. The response is in line with the severity of the action.
But... if you say, consistently piss in the elevators of your local metro (even though public bathrooms are available), most folks aren't sure prison is the right answer. Ideally - we'd just keep you out of the metro entirely - but setting up that system is very expensive when we're dealing with a very small number of bad actors.
On the flip side - that small number of bad actors is doing considerable damage long term. They're making metro usage far less pleasant, driving down ridership, increasing cleaning costs, reducing public health, and requiring additional staff in attempts at monitoring. Each other member of society is only inconvenienced a relatively minor amount, but they're impacting a very large number of them by degrading a public and shared service.
The same is true of those who camp/sleep outside of businesses, or scream & rant in public spaces, or do drugs in public spaces. They are actively harming the space they are using at large, and are unwilling to stop or unable regulate themselves.
So what do we do with those people? What is a proportional action that we can take that prevents the damage this person is causing at scale?
Prison/Jail rarely work - because the damage of each individual occurrence is small, they are usually out very quickly.
Providing housing can resolve problems in some cases, but there are people who are actively unwilling to stay in publicly provided housing (for a variety of reasons - although the most common I see is consistent drug use, closely followed by serious mental illness).
Meds can definitely help - but the category of people creating these disturbances generally have trouble consistently taking meds (again - for a variety of reasons including access to services and payment, but not the least is active, personal resistance)
So... if we've ruled out (as in - tried and failed) self medication + housing + prison... where do we go?
Because at that point - I'm not really convinced that forced treatment and care are really unreasonable responses. It is far more cost effective to gather these folks in a single place and confine them there than it is to allow them to roam and attempt to stop their problem behavior at the place it occurs. It's the difference between 10 guards, a large facility home, and medical staff - versus thousands of required staff spread over a city.
Why don't we see what happens when we max out this intervention? Data seem to show that it would free up a lot of resources, and maybe some of those whom you're assuming will be recalcitrant won't be if housing options are ample.
I think it's likely this would address 80% of the problem, and then we can see what the remaining 20% looks like qualitatively and quantitatively.
I do agree that mental illness definitions are a problem. Even forcing treatment on just those who are a danger to society makes me leery given that hostile social posts are now a social danger.
I also think that there are a lot of 'low-hanging fruit' level of options available, that seem to be disregarded in today's all-or-nothing environment. Specific example: During my short, ~10-block drive to the 101, I pass a good half-dozen regulars who are either screaming at the aether, wandering erratically through traffic, flinging things at passing people/cars, or in one case literally rolling around on the onramp between cars. This is not an exaggeration, or hyperbole.
These people need to be in an institution. Maybe with treatment, they can recover. Maybe they will be there for the rest of their lives. Maybe some form of halfway-house works best. But I can't think of any good-faith argument that leads to the status quo being the best choice for either them or society at large. Surely we can come to a societal agreement about what to do for this level of dysfunction?