Maybeeee, except then you wind up with a service class of workers who can't live anywhere near the places that need servicing and they have no way to get there.
Unless you're going to bus them all in from afar, it doesn't work. And why spend a long time on a bus to do a low-paying service job when you can just walk down the street 10 min and do the same low-playing job? Why waste time on travel to service the rich who let the free market boot you out when you can service the average nearby?
Here in Phoenix, a 1-bdrm apartment in the ghetto is $1200/mo. Plenty of new apartments being built, all around, and every single one of them are "luxury" apartments.
Doesn't help the problem.
Scottsdale is pretty hoity-toity....where do you think their service workers live? Not Scottsdale! But it's not a peninsula with limited space, so all the service workers ride or drive in from the surrounding, poorer areas.
Hell, you could make the argument that Mesa is a 1,000,000 person service city. Poor, run-down, but adjacent to nicer parts of town.
Hooray free market!!!
Now the poor can have worse infrastructure and worse schools to maintain their role as service industry to the wealthy!
MISSION ACCOMPLISHED!
Well, the market should determine the prices. If the businesses COULD NOT get any workers, the pay would go up, otherwise they would have to shut down. Can we agree on that much? In fact, I've known businesses that could not get workers and had to shut down. No workers = no work.
But cities create red tape, NIMBY policies, unnecessary regulations, excess permits, the whole 9 yards of bureaucracy that limit housing options. Limited options will always result in high prices. This includes rent control and AH, they create artificial markets that influence the real market.
What I'm trying to say is what would fix a lot of this is less regulation, not more. Because as long as the gov't steps in and creates artificial influence on the market it will always result in a worse condition for the very people they are trying to help.
This is not a perfect world, and sometimes people will have to endure shitty circumstances. Some people grow out of it, and some never do and sometimes (oftentimes) it is their own fault. It's not the gov't responsibility to ensure "life, liberty, and pursuit of happiness". It's only their role to ensure that you are able to pursue it, not guarantee it. The very fact that the more gov't involvement in places like CA and NY result in population migration to places with less taxes and regulation is evidence of this.