http://missingmiddlehousing.com/
Just as one data point, we have torn down more than a million SROs in recent decades while population has risen. SROs used to be a normal form of market rate housing that worked well for people just starting out who didn't have much money and didn't need much space because they were single and childless.
https://en.wikipedia.org/wiki/Single_room_occupancy
We also need to resolve the health care coverage issues in the US. Health insurance eats up a high percentage of the US GDP. Most homeless people have serious health issues, either physical health or mental health issues.
This is a significant contributing factor to homelessness. There are studies that show that when people get affordable health coverage, it reduces the risk of eviction.
https://www.benefitspro.com/2018/12/14/one-side-effect-of-th...
We don't need "homes for the homeless." We need homes for the people. We currently tend to build homes for rich people only and basically shrug and say "not my problem" when the rest of the US can't make their life work.
Then we act like homeless individuals are simply defective individuals and weren't screwed over by a broken system. No, they just need to stop drinking/using drugs, obviously. "It's just a personal issue."
Never mind that new housing has more than doubled in size since the 1950s and added substantial additional amenities at the same time that the average number of occupants has declined. These changes in housing pushing up housing costs couldn't possibly be related, no. Ask anyone with a good income and cushy life.