Being more tolerant of the homeless population than other cities or regions could certainly encourage some homeless migration. So could more moderate weather. But housing affordability (costs relative to incomes) is a pretty big deal too.
Housing costs depend on a few things, but supply/demand is probably the biggest part of a fairly complex puzzle. High prices come from more demand than supply. Everybody competing for a limited number of houses in a limited amount of space leads to massive price increases. If you put everybody into SFHs, then you get sprawl. Sprawl means you need more infrastructure, and you get fewer tax payers per acre/sq mile to support that infrastructure. So the result is shitty roads, less school funding, less policing, etc. It also means that people have to have a car to get around instead of public transit or walking. That transportation costs money from the individual, so you get into a dynamic where you can only afford to live way outside of the city, but (a potentially large) part of those savings are eaten up by transportation costs. This goes on long enough, and you get entire regions that are unaffordable for lower income people.
SFH owners in these locations aren't likely to want more dense housing options because it hurts the value of their property. At least until they want to sell, and a developer offers them over market.
A healthy city needs workers of all income levels to function. (For the time being) you need people to serve food, clean hotel rooms, staff daycares, etc. Those people have to live somewhere, and in most of these big cities that can be difficult. Example:
SF
had median per capita income of $68k, and median household income of $112k for 2019. They had a 10% poverty rate.
The median home value was $1.1million (9.8 times the median household income). Median rent is $1895/mo (33% of median per capita income and 20% of median household income). So home ownership is super expensive and likely out of reach for most, but renting doesn't seem too bad. Their homeless rate per capita is 397 per 100k residents.
LA had
median per capita income of $34k. Median household income of $68k. 13% poverty rate. Median home price of $583k (8.5 times median household income). Median rent is $1460/mo (50% of median monthly income per capita and 26% of median household income). So home ownership is out of reach for most
and rent chews up a large part of what is relatively low income. Their homeless rate per capita is 400 per 100k residents.
Detroit (Wayne County,MI)
had a median per capita income of $27k. Median household income of $47k. And a 20% poverty rate.
The median home price is $113k (2.4 times median household income). Median rent is $875/mo (39% of monthly per capita income and 22% of median household income). Homes are much more affordable. Rent is about on par with SF as far as % of take home pay though. Can't find the rate of homelessness specifically for Wayne County, but Michigan as a whole is about 80 per every 100k residents.
So, when I look at that data I see that the CA cities have far more expensive housing. But SF has high enough incomes that lots of people can at least afford rent, while LA does not. The rate of poverty in these 3 locations actually increases as you get cheaper, but homelessness moves with rent/income ratio and price of buying a home. Like I said earlier, there are a bunch of factors that play into it, but I don't think it's a coincidence that the place with the highest poverty rate has the lowest homeless rate. I think that's primarily driven by the fact that people at or near the poverty line can still afford a roof over their heads. Michigan is in a sweet spot of being cheaper to buy and still having a decent rent/income ratio, so homelessness is much lower.
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