There is an awesome book called "How to lie with statistics." I highly recommend it. Your quotes of median incomes, etc, are very much in that vein, especially given that it is in a discussion of how to house the thousands of homeless people in LA.

The history here in the US is this:

We had The Great Depression in the 1930s. People were incredibly poor. This was followed by WW2.

The men went off to war. The women got factory jobs. They stopped building cars when they converted the car factories to jeep factories. Luxury items like sugar were rationed. People were encouraged to grow Victory Gardens so farm food could feed the troops.

The result: Two income couples with no opportunity to create babies and no means to spend all their money. Savings rate were as high as 50% during some parts of the war.

The war ends. Soldiers come home. Women quit their jobs en masse to go be wives and moms.

Soldiers get help purchasing houses. They get help going to college.

There is both huge pent up demand for middle class housing and also the means to buy it. The entire nation rises to the occasion to roll out houses. They invent financing mechanisms, etc. Houses get built at breathtaking speed. The modern suburb is born.

Their children, the Baby Boomers, reach adulthood in the 60s and 70s. SROs and boarding houses had been the standard answer for single young adults with entry level jobs. This generation had unprecedented upper class style wealth. They turned their noses up at SROs and the like. The US tore down about 80% of them.

US housing stock skews strongly towards housing designed for a nuclear family. It is strongly shaped to this day by the 1950s nuclear family expectations, only on steroids for various reasons. The size of new houses has more than doubled since the 1950s and we expect a lot of amenities that were not the norm at that time.

Meanwhile, demographics have diversified and moved away from the nuclear family. People are having children later. We have fewer children on average per family. We have more single adults, single parents and childless couples. Yet, our housing expectations default to 3 bedroom, 2 bath house in the burbs type housing. It doesn't even fit the demographics.

We now by default expect single adults to rent a two or three bedroom place designed for a family and share it with room mates. There is damn little actually designed for single people or childless couples.

Our housing is designed for a population, culture and lifestyle that mostly no longer exists. This is the crux of the problem.

As I find things that actually work, I blog about it. I am actively encouraging homeless people in So Cal to leave and go to either cheaper parts of the state or go to another state entirely. Going to the Central Valley did not get me off the street, but it did improve my quality of life. Leaving the state did get me off the street.

There is currently a deadly hepatitis epidemic killing homeless people in So Cal. If these people had a solution, most of them would be out of there like a bat of hell. This problem is quite dire. More actual affordable housing would not magically solve it overnight, but it would be a step in the right direction.