So you risk getting into "revolving door" admissions to hospital. A person with a psychosis becomes ill, rejects medication, is detained against their will in hospital and given medication against their will (sometimes by force) until they "become well" enough to be let out of hospital. At which point they're free to decide to stop taking the medication.
I'm not sure that this style of revolving door admission is better for the person than just letting them be homeless. (Although preventing people getting into that situation would be a good idea).
This already happens with homeless people: they become diseased, malnourished, get drunk and hurt themselves. Once the trauma has reached a certain degree that they require hospitalisation, they end up in hospital and released once they've recovered. Are you proposing we not help them at all and just let them fester and die on the streets?
Surely not. The "revolving door" concept, as you call it, is the middle-ground between not helping at all, thus letting a mentally ill person reach trauma more severe, and permanently confining those with incurable mental disorders (but those which can be controlled, and the patient able to live healthily outside the ward), which is both wildly expensive and harder to justify overruling the patient's will and freedom.
No, I'm saying that you can't force people to take medication against their will apart from a few situations.
If you want to provide MH treatment to people it's much better to start with children and young people and better drug and alcohol services, both of which would reduce the amount of homeless people, and also to provide better voluntary MH treatment for homeless people.
People aren't arguing with you because you want to provide MH treatment. People are arguing with you because you want to force that treatment on people against their will.
So you risk getting into "revolving door" admissions to hospital. A person with a psychosis becomes ill, rejects medication, is detained against their will in hospital and given medication against their will (sometimes by force) until they "become well" enough to be let out of hospital. At which point they're free to decide to stop taking the medication.
I'm not sure that this style of revolving door admission is better for the person than just letting them be homeless. (Although preventing people getting into that situation would be a good idea).