Ironically, the most recent survey in the special unhoused enforcement zone near me found that the number of people living on the streets was almost identical to the number of empty beds at the shelter.
I think a bigger factor is that the tiny homes limit how much stuff you can bring (aka 1 bike per person, cant build your own structures on the land, no drugs, etc), which seems to be the most common reason people gave for not wanting to go.
One: many homeless people feel dehumanized by how they're treated by the staff, and
Two: homeless shelters are full of homeless people
You are not describing any homeless shelter that I've ever seen. Usually they are very crowded communal sleeping facilities with barely any security and zero privacy. Theft and assault are a common occurrence.