The properties for sure are nasty, but remember that we're trading nasty streets and nasty parks for an occasional nasty apartment. The one article quoted $8000 in one-time damage cleanup which is chump change in the scheme of things for someone owning a dozen units or more.
While I think the occasional trashed unit needs to be accepted to solve homelessness, cleanliness issues can be solved by having support monitors regularly check in and help tenants get into a habit of cleaning up after themselves and their guests.