Maybe in a Utopia the homeless would use shelters but many refuse to for very reasons.
My understanding is that the vast majority of the homeless in NYC do sleep in shelters because... well, NYC has plenty of shelters.
So there might be a small number of homeless folks who can't / won't live in shelters, but that's what it is: a small minority.
[0] https://www.sfgate.com/bayarea/article/Bay-Area-homeless-uns...