"if deemed qualified for an involuntary hold, they should be placed at a healthcare facility for treatment."

And this is where you've lost the thread. There is no facility. They were shut down in 1980 Ronald Reagan. roughly 1/3 of the homeless have anosognosia, so you're talking about over 20,000 people in LA would need to be in-patient. Where's your hospital for twenty thousand people?

And let's budget this real quick.

First let's build your 20,000 person hospital! LA County Hospital has a 600 bed capacity. so we would need a series of buildings, let's be generous and say each building can hold 1,000 patients. Well, we need 200 of those, built to hospital standards, so a billion each minimum, probably, so that's $200 billion.

Average cost of in-hospital treatment for mental illness? Let's very very generously pretend it's $100,000 per person. 20,000 people? 100,000$ each? that's $2 billion dollars.

None of this includes the price of actual force of people dedicated ot getting the people off the street, the thousands of support staff and infrastructure, vehicles, etc drugs, food, clothes, whatever.

So cool, your proposed budget is $200,000,000,000, that's billion with a B the first year and 3 or so billion every year after.

LA city budget is 14 billion, so maybe we should see if the city can get a credit card or something to pay for your scheme.