This is not the way mainly because the state does not have the resources to satisfy all housing demand (but also because two-tier rental markets are really unfair to newcomers). What we need is radical reforms in permitting and regulation at all levels of government (but especially at the local level). Imo the main obstacle to these reforms is that it is too easy to shout them down with talking points like "neighbourhood character", "lawn space", "shoeboxes" or "greedy developers".
If North American cities zoned a quarter of their area as 5-story midrises with large parks and mixed use and made permitting quick and easy we could really bankrupt the rent-seekers.