This has always felt like one of those arguments that just kicks the can.

Yes, there are 100% some homeless people who are in such a bad place that they'd outright refuse a home even if you gave it to them free of charge (or would immediately sell it for drug money/burn it down because it's filled with alien Spyware or something), but I'd wager that if you actually gave a lot of these people a stable home, and food in their fridge so they weren't literally fighting for their lives on the street, they'd be able to self improve a lot more than people give them credit for.

A lot of homeless are just people who had one bad turn after another and are just unable to break the cycle because our system really isn't built to let them do so. I think we should also be providing mental Healthcare and addiction support to these people, but saying that should come before giving them a sense of stability and safety is ass backwards imo