If even 1/3 cannot find proper housing why would anyone want to accept the offer of temporary shelter?
Isn’t it much better to setup a tent somewhere where you may be able to live for weeks, months, or even years without being kicked out, as opposed to the temporary housing where you will be kicked out in 14 days max.
The homeless don’t make decisions in a vacuum. A large part of the reason they declined is because they knew that if they accepted they were only delaying the inevitable.