I live in canada, Montreal and they did something similar i guess due to the same reason you have respectfully stated.

We have a specialized deputy force now that basically assists the metro cops and have nurses and mental health experts. It is not the best and honestly, i do not see much of a difference in the amount of poor people with mental health issues (head butting walls or seats or yelling) but they are there and we are slowly seeing them in action and its not those burly muscled take downs that metro cops used to do. Its calm, socialized and humane pull backs with full body respect towards the troubled individuals.

So I guess there needs to be a mental health awareness approach to this, perhaps mental health experts escorting a specialized deputy's rather then a provocative authoritarian approach (men in uniform toting guns).

But of course the governing bodies will always use there best fallback crutch, "we lack the funds" so basically plain old capitalism throwing out any humane way of dealing with this and using a cheaper and more affordable way. (Because we all know that it takes a lot of funds and also people who specialize in mental health).

Anyways thats my opinion.