Demand currently outstrips supply. As long as that continues to be the case, the housing crisis cannot be solved.

That said, you're correct that this isn't the only change that needs to be made. If you increase supply without raising taxes on homes past your primary resistance, you just encourage rental companies and investment portfolios to gobble up the new units so they can control prices and keep people renting. Building more houses and apartment buildings is a necessary step, but it's one part of a system of related changes that we need.