Housing is expensive in desirable places. These areas are also traditionally quite affluent and liberal -- because you need to be relatively rich to live there. As a result, they tend to be much more accommodating to the homeless and addiction. That doesn't mean housing prices in LA/SF/Miami/NYC are the reason homeless people gravitate there but it does explain a correlation.
These are just unsupported assertions unless you can disprove the wide body of research I linked to that demonstrates rates of homelessness and housing affordability are strongly correlated. Many “red” cities and states have higher rates of drug abuse, mental illness, and crime, but less homelessness. Why? Because housing is affordable in those places so people do drugs and have mental illness while sheltered. It’s honestly not that complicated. It seems like you’re trying to obfuscate these documented realities to suit your own narrative.