The homeless support systems can't take on more homeless people.
Being homeless isn't just the absence of an apartment or a house. It is a grueling, emotionally and often physically painful life. It is continual stress. It makes healthy people sick and sick people sicker. It frays and destroys friendships and familial relationships. Many people who fall into homelessness deteriorate and don't recover.
It will be less expensive for the government and less of a strain on other systems to stop all evictions.