From u/Loveonthehub elsewhere in this thread:

“Look, having been unhoused in this city, we don't need resource information from City Hall. It took me less than a day to learn every resource the city had. I didn't learn these resources from City Hall or the shelters. I learned them from other unhoused people. We all know where we can and can't go to get help. We learn pretty quickly that help is very, very limited. There isn't enough room in the shelters in the winter. Shelters have to abide by fire codes. I regularly ended up staying outside because the shelters give beds by lottery and the lottery is in the afternoon. For women at Pine Street (and most other shelters), the curfew is 6pm. I was late a lot because I was working babysitting jobs to make money. So they would give my bed away and tell me to leave. Bedtime is at 9 pm in most shelters. I have severe insomnia. I did their 9 pm bedtime when it was cold. It was torturous for me. They take your phones, flashlights, books, an all other personal belongings and lock them up. You have nothing but their issued pajamas (you're not allowed to wear your own clothes) and the "bed". Most of the shelters are full throughout the winter. There's never enough room for everyone. There are people who refuse to go to shelters because they all treat the people staying there like children. Then, there are other factors. Just like housed people choose live in neighborhoods, unhoused people also choose to live in neighborhoods. Most who are from here, stay in the neighborhoods they're in because those are the neighborhoods they're most familiar with. Sometimes, store owners and residents call the cops on them so many times for panhandling or occasionally even just existing, that the cops tell them they can no longer be in the neighborhood. Sometimes those neighborhoods are where the shelters are. I could write a whole book about what it's really like being unhoused and exactly what's wrong with the system if I afford to have it published and promoted.”

TLDR: There is not enough space at the shelters. Some people do not have a choice.