I don't see how this is the hospital's fault: they can't keep patients indefinitely. Today's Washington Post has an article on the increasing number of homeless seniors https://wapo.st/3q8Gzeb which includes this passage:
"After treatment for an acute illness, hospitals often discharge homeless patients, who wind up back in shelters or even back into their sidewalk tents and makeshift lean-tos, in what health practitioners in Phoenix ruefully call “treat-and-street.” ... A pinball effect takes hold, said health-care providers, shelter operators and advocates. Homeless people bounce from homeless shelter to hospital, then to a nursing home for a short-term recuperation stay. Once that short-term stay ends, nursing homes must decide if the person is infirm enough to qualify for long-term care. If the answer is no, they must leave the nursing home, starting the cycle over again."
I would consider it VA not being an example of "it works fine" if they can sometimes get some help after waiting a long time, then get dumped out in the street to rot. Maybe the specific hospital itself isn't at fault, but the program in general is contributing to the exact issue you're quoting, which is more or less what I'm talking about.
Seems to me it is a poverty support/housing problem, not a healthcare problem (which, sure, impacts healthcare, in the same sense that poverty/housing issues impact education and pretty much every other aspect of society.)
"After treatment for an acute illness, hospitals often discharge homeless patients, who wind up back in shelters or even back into their sidewalk tents and makeshift lean-tos, in what health practitioners in Phoenix ruefully call “treat-and-street.” ... A pinball effect takes hold, said health-care providers, shelter operators and advocates. Homeless people bounce from homeless shelter to hospital, then to a nursing home for a short-term recuperation stay. Once that short-term stay ends, nursing homes must decide if the person is infirm enough to qualify for long-term care. If the answer is no, they must leave the nursing home, starting the cycle over again."