I'm not sure they'll even drop if building codes are relaxed. After all, those SFH owners also own the land beneath their house. The price per square foot of living space could drop while the price per square foot of land goes up.

Any change will take 20 years to start working through the system.

That said, prices will change. SFH owners move once in a while. Even if you live in the same house for 50 years (about the max possible given human lifespans), someone else on your block will move every few years. When someone moves a developer will look at the location and decide if it is wroth buying the house for the lot, tearing down and building something else. Right now in the Bay you could buy a lot of SFHs, tear them down, replace with a 10-plex and rent it out for enough to make it worth it. (Assuming zoning codes would allow this without a large cost over the cost of labor and materials) Eventually though housing will catch up and rent will fall until it isn't worth it.

We can't prove the above because of course zoning codes won't let you do it.

> There are way more people that want to live in these places than houses available.

That's like the saying "government bonds are 0 risk." It's usually true, til it isn't.

These problems with housing costs in these cities absolutely will make the cities less desirable, I think we will see a large deurbanization period in north america very soon and you'll see most of these cities that are constricting supply of housing crumble like Detroit.