What happens next? Just no more homeless?
No, more homeless will appear. They will fill the same corners and tents that you just cleared the month before.
This is not a solution. This is a grift.
It's not like they magically respawn or something. There are people who have studied the root cause of homelessness, and: it's housing. Sure, other factors make things worse, but there's more homelessness where housing is expensive.
Which stands to reason: when a thing is expensive, fewer people can afford it.
https://homelessnesshousingproblem.com/
That's why, ultimately, the biggest YIMBY win is going to be not helping out people currently homeless, but stopping the pipeline in the first place by having enough housing.
If free, safe lodging is available without restrictions, demand will quickly outstrip supply with folks moving from other cities (LA, Seattle, Portland, etc) to fill the available rooms. It's a $50 bus ticket, city officials will likely fund these tickets for them to get to SF to take advantage of this. SF had programs for this exact thing to get homeless out of SF [1]
1 - https://www.vice.com/en/article/bvg7ba/instead-of-helping-ho...
Housing homeless people reduces overall homelessness. If we do it enough, everyone will be housed. Part of this is lowering housing prices, another part of this is housing people who can't house themselves (for various reasons).