I think you've inadvertently explained why SoCal in general and LA in particular have the homeless and recent public health issues they do. The defeatist attitude that says "if we run them off they'll just come back" is part of the problem. There are laws against loitering and solicitation and creating a nuisance, along with penalties for each of those offenses. But if no one is willing to enforce the laws which already exist (for whatever reason), then they are useless.
From what I've read much of the current homeless problem can be traced back to the time of (governor and president) Reagan pushed for wholesale defunding and dismantling of the long term mental health industry. I think many people would agree that there were a lot of problems with how that particular industry was run and regulated, but by choosing not to replace it with anything better a new problem of rampant homelessness and perpetual incarceration was born.
I travel to the west coast often and SoCal on occasion and this major issue has only gotten bad in the past five years or so. Blaming this on Reagan from over 40 years ago is silly. Just looking at the people who are causing these issues, and I was just in Seattle several weeks ago and saw these problems in WA first hand again, almost all are between 18 and 35 years old, some of whom were openly shooting up on drugs in the middle of the day on the sidewalks in downtown Seattle. The police finally stepped in, after several of the addicts began going after people walking along the sidewalks. Not the "traditional" down and out old guy or gal who was a refugee from a mental hospital or a chronic drunk by any stretch of the imagination. Granted I am looking at a small sampling of people in my travels, but I didn't see any "drunks" or open or empty liquor bottles, just lots of needles and drugs. And what I saw in the heart of Seattle in the middle of the day was virtually the same as I witnessed in LA and SF. As much of a rail fan as I am, I think California's billions would have been much more wisely spent on helping these really sad examples of humanity, rather than building the HSR to nowhere.