My county has bought up hotels to house homeless. They own seven or so which can host over 700 people. While great, it is still only a fairly small chunk of our roughly 40k homeless.

People are fairly sick of seeing so much homelessness and think a shelter bed fixes the problem and if a homeless person rejects that bed, they simply want to be homeless. A shelter bed is a very temporary solution. Shelters are often run by religious organizations that can have pretty strict requirements (be in line at a specific time to get a bed and be out at a certain time) and can be hostile to some group's lifestyles (can't be with your partner, hostility to the LGBTQ community, etc). They also are not super secure for your stuff and can be violent. It is not too surprising that only a little over half get a shelter bed after a sweep (although it is never stated whether the beds are rejected or there just is not capacity).

It sucks. Often one city will offer some small amount of services and then homeless sweeps by nearby cities drive the homeless to the city offering services. We also get people sent here from other states via one way bus tickets.