It hasn't been disproven. There being more vacant homes than homeless people just means that the market isn't clearing, because the minimum price acceptable to the landlord is higher than the maximum price acceptable to the homeless. This could be from any number of reasons, none of which "disprove" the fact that the laws of supply and demand do in fact apply to housing.
As an analogy, there are always jobless people even when there are vacant positions to fill. Why? Because of a mismatch between the price of labor, which is artificially inflated by minimum wage laws and another hundred laws and regulations that make it costlier to employ someone, and the economic value generated by that labor.
Who cares if there are vacant homes in downtown Detroit for sale or rent? If you moved there you wouldn't be able to get a job
And as with many other ways to make a living at the expense of society - such as fraud, theft, and abuse - it should be illegal.
- there is a housing shortage
- as a society, we should make sure that resources are available for the ones who need it most
- people who earn more money, deliver more value to society (not necessarily true of course, but well, capitalism)
- as a society, houses should be available for the highest earners first
Therefore, everyone should increase prices as much as possible. Until you cannot sell or rent to anyone, then you lower slightly until you can.