You have to be a complete moron if you think the problem isn't enough supply.

The population of the US is growing. And the percentage of people living in cities is rising. That's lots of people looking for housing in cities. At the same time, single-family zoning (which account for around ~80% of land in US cities--before accounting for industrial and commercial) prevents the development of more housing. Old neighborhoods are effectively full, mostly owned by the same families that bought them in the 70s through 00s. New development is waaaay out on the fringes of the city, and expensive as hell because it's in such high demand.

There isn't enough new housing being developed to satisfy the growing demand for housing, so prices rise. It's that simple! The problem is exacerbated, because the rising prices attract investors (corporate and private) and AirB&B etc. But the fundamental problem is that most of our cities are seas of already-occupied single-family homes, and at the same time populations are rising. This is obvious.

But politicians love to blame foreigners, immigration, corporations, AirB&B. You know why? Because the root of the problem is middle-aged surburban majority-white families that don't want more people (with associated traffic, noise, whatever) in their neighborhood. And that's their core voting base. Old white people vote like clockwork, young renters reliably don't. If politicians go on a crusade against the single-family-dwelling suburbs, they know they'll get voted out. So they throw you these stupid bones: "it's the Chinese who are making housing expensive, by buying 1% of units (and mostly living in them)! It's AirB&B, with a few thousand units for rent in a city of 6 million people! It's the corporations, doing...things nobody can quite explain, that somehow involve buying housing and then just letting it sit there unoccupied? Or something?"

You're a sucker, believing that bullshit. It's the voters (the ones who actually vote) who are the problem.