Yeah, but I think those are going to be small effects. You'd want to try and encourage people to move to smaller cities to really move the needle I think, but obviously the larger cities aren't interested in that. And the jobs have to move with in some fashion for it to work and everyone likes having access to larger pools for labor too

I assume most people owning multiple residences are renting out the extras. What you are describing would make more houses available to buy at the expense of having fewer to rent. This wouldn't be a net gain of available housing.