That's not true at all.

The government could crash the house prices overnight if they wanted, for example they could implement a 20% yearly tax on home value. Prices would plummet instantly because owning a house would cost a lot more, the increase in yearly cost needs to then be offset by a drop in the fixed cost (selling price) to bring back equilibrium at the current supply level.

It also increases supply massively without building a single new house, because the bigger your home, the more tax you're going to pay and if you aren't using it you're likely going to sell and downsize immediately to save money.

The best way to do this would be then to take all that massive tax influx, and remove income taxes entirely or provide a UBI to everyone.

There are other ways to achieve similar price reductions overnight too. The problem is that it's political suicide to crash the housing prices, since home owners would be absolutely pissed if you just kill 50-75% of their home value overnight. That's hundreds of thousands of dollars for most owners, and 65% of residential properties in Canada are owned by the family that lives in them.

It's a fallacy that there isn't enough housing, there are already way more bedrooms in Canada than people, and on top of that a large portion of people share a bedroom with their significant other. The problem is the distribution of housing (both in terms of who owns it, and where it's located) not the total.