This solution makes me really uncomfortable.
You're completely disregarding the individual and saying that we are responsible for creating an environment for them and ultimately, we are responsible for their behavior.
These are independent, adult people who are perfectly capable of making their own decisions, good or bad, and living with the consequences of those decisions.
It shouldn't be the public's responsibility to remove them from neighborhoods or 'build them houses and put them there' as you said.
If low income people want to live in one of the most expensive areas in the world, they can. But they shouldn't expect to live well.