That's what people are doing in gentrified neighborhoods. The natives can't earn a livable wage anymore so they move out. The problem are the ones who chose to stay then became homeless. Once you're homeless it's harder to get out of it because nobody wants to hire a homeless.
You need money to move to another location and rent the first few months while you're looking for jobs. Also, you might have families and friends in your current location. It's kind of unfair to ask them to move to a new location. You might go East but I might go West. Lives are going to be altered no matter what.
As for homelessness it's people enabling them. There's a reason why so many homeless/panhandlers are coming to CA because of the benefits. There's a reason why the benefits aren't helping them too. They're unorganized. There are like 5 different organizations all doing the same thing. The city pays these org to feed and cloth them or whatever. Because each organization is a separate entity, a lot of times they end up serving the same homeless person twice. Org A gave food to hobo1. Org B didn't know Org A fed him already gave hobo1 more food. Then you have other people waiting in queue starving while hobo1 is being overfed.
To solve the homeless problem, you need a more organized way of serving them. See above.
And 2 leave it to the professionals. Do not give money or food to them. They will become reliant and no incentive to get out of it. After awhile you just get used to it. They're getting so much money that you have real people pretending to be homeless and panhandle on the street. A few admitted to raking in 6 figures all tax free.
It's obvious these guys won't be able to survive in an expensive ass place like CA but why so many come in every year? SF and LA especially. It's because of enabling people. I work with the city and naturally the shelters and homelessness. I see these stats. Every year the city removes about 5k people off the street but another 10k enters. Once they organize all these different organizations it will be a lot more effective.
But the problem is why are they entering homelessness in the first place. Mobility is one solution. The government are sending homeless people elsewhere. There are too many factors and we need to look at them all. But your theory is a small part of the solution to a much bigger problem.
In the meantime, please do not feed or give money to them.