Seems to me like the people who win the most by limiting housing are the landlords who can collect higher rent through scarce supply.
Long term homeowners probably don't care much about yearly changes in their homes worth.
They'd probably be fine with more housing being built 'somewhere else' for the homeless. But ya know, definitely not in THEIR backyard.
Developers (aka landlords) aren't the ones protesting new building being built. This is because they would love to be able to build more. Even though they would make less money per apartment, there is so much demand for houses, that the massive amount of new development would make up for it.
There is only so many landlords out there. Their vote isn't particularly significant. But there are a LOT of NIMBY homeowners.
My point is that homelessness severity in any given area is correlated with renter density.
Whatever homeowners you think are blocking new developments, think about the homelessness in their specific area. Is it severe?
Think about the areas in SF that have the most severe homelessness, how many homeowners do you think live in that area?
On the causes of homelessness... I don't think it's due to scarce housing. Even if there were more housing available, I doubt a homeless person could start paying for it. Getting out of homelessness is a more complex issue.