> Programs which have offered the homeless real homes, with privacy, the ability to safely store belongings and keep pets, and the ability to decorate, cook, and sleep in quiet, have not had any difficulty filling those homes, but these programs are few and far between (none exist in the US, that I know of).

This one is close to what you're describing:

https://www.lihihousing.org/tinyhouses

(Consider donating!)

These tiny house villages are real tiny homes, providing privacy & dignity.

And you're right about people preferring anything over a shelter:

"Some of the people we spoke with told us that if given a choice between staying in a nearby homeless shelter or spending their nights in a tent, they will choose the tent" (https://www.krem.com/article/money/economy/boomtown-inland-n...)

A tiny house in a small-by-design village is a better solution than a tent in a large encampment or shelter.