Perhaps the problem is that there IS a govt welfare program. The complaint currently is that what’s being done is not enough. The truth is that it will never be enough. The govt and tax payers can shovel mountains of dollars into the maw of the problem and it will never be enough.
The way American welfare programs are designed is like sticking a band aid for cancer and hoping rosy health will return.
If we stop relying on govt, perhaps our tribal instincts to care for each other will return ...perhaps it will finally dawn on us that we rely on our kith and kin...that we come from other people like us and it was not the govt that birthed us.
I don't think that's true. Welfare as commonly understood doesn't really exist any more in the US. The closest is TANF (temporary assistance for needy families) but that requires you to have children and is time limited. SNAP gives you food benefits but that is limited to 3 months unless you have a job or are in workforce training. For the most part, your random homeless person on the street isn't eligible for these and doesn't get benefits. The loophole is disability but that's a pretty tough process to go through. Not likely that many homeless can muster it.
I've no doubt that, for every person who ends up rough sleeping in the US there are 1000 who move back in with their parents. Or sleep on a friend's couch. Or get gifted a few hundred bucks from a loved one to tide them over. Or move in with a partner when otherwise they wouldn't have.
But there will always be some people who don't have any social connections left to spend - if your parents have died, or were abusive, or you're a first generation immigrant, moving back in with them might not be an option. Maybe you've had $300 from grandpa several times before, and lost it to your gambling addiction. Maybe you've stayed with your sister before and scared them with your untreated mental illness.
None of which is common - but if a million people are struggling to make rent it's a simple numbers game: some of them won't have any social connections to fall back on.