I think this is the problem left-wing/liberal/socialist thinking. It sounds great - nobody should be on the streets - we have enough resources to house everyone. And then a little while later it's some kind of totalitarian nightmare with people forced to live in institutions as you think you know better for them, and anyone who doesn't agree with your way of life must be insane.
As a left-wing/liberal/socialist, I both believe nobody should need to be on the street, and that it's totally unacceptable for the state to use force to put people in institutions without very strict checks on mental competence.
I find your notion that there's some slippery slope where we'll suddenly want to force people into institutions quite bizarre.
A lot of socialist thinking, on the contrary justifies the need for a welfare system and redistribution with arguments that true liberty is only possible once there are protections in place which ensures that you do not just have the legal opportunity to make your own choices, but also the means to realistically be able to make choices.
On that basis, the argument both for giving people help to get off the street and restricting the states ability to interfere if you chose untraditional lifestyles is the same: Maximizing liberty.
Now, given the old socialist joke that if you put two socialists in a room, you'll get three incompatible definitions of socialism, there may be socialists out there more gung-ho about institutionalizing as many people as possible, but I've not met any.
Conversely I'd hesitate to say it's a right wing issue, despite the fact that historically a lot of right wing governments have been very gung-ho about using draconian measures to force people off the streets and into institutions, including the use of police to remove them coupled with work-houses or even prison next to mental institutions, as many have had a long tradition of seeing homelessness or poverty in general as a sign of moral failings that need to be treated harshly.
