There is only a tiny fraction of the housing required. There is single digit percentages of the actual housing required and low to mid double digits percentages of shelters where some of the time if you get their in time you can sleep in a communal space where you can't bring your belongings, your pets, cohabitate, where you might get raped, or acquire new 6 legged friends, or more recently covid before being turned out in the morning.

It's not like most people are being offered a job and an apartment. They are being asked if they would like to be warm for 10 hours and even worse off than before.