Earlier quoted context omitted.
Raising taxes on the land owner will result in increased rents. Land owners are not in the business of giving money away.
Taxing unoccupied homes lower rents, obviously. Also taxing income progressively discourages landlordism. On top of that, taxing income in order to build public public housing lowers rents even more.
This doesn't happen because those who have a political say don't actually want more housing. My proposed idea would force the government to actually solve the problem after all. If there is not enough housing the government would be forced to build it as a last resort and if the government can't do so because of the laws it has enacted then it can change those laws but that's exactly what must be avoided at all costs if you were to ask existing homeowners.