The population would not be increasing dramatically if we stopped letting more people into the province.
Well... i'm going to have to concede that point at least, the math is certainly on your side "_
Therefore we would need to build far fewer houses
And we would. The way our system is set up we will always build fewer homes than we need. It's not INTENTIONALLY set up to do that, but that is the outcome. For several reasons. So the problem woudln't change. We still wouldn't build enough homes and we still wouldn't keep up with demand. We just don't build enough homes. The only thing that would change that is if our population steadily decreased over a long period of years and that would leave us with a host of other serious problems.
Remember - the number of homes we build HAS increased - it's just always increasing slightly behind population growth so the problem always gets a little worse. But it's not like we couldn't build more - we did increase. And we could easily do a massive increase if we wished now. But - the way things are that is seriously discouraged from happening on many levels.
and the cost of building would drop dramatically.
It would actually go up. But not by that much so it's not really a big deal.
The thing is, we do need population growth. Whether it comes from immigration or natural internal births, we need to grow. For several reasons. So simply stopping growth is not a workable solution. Reducing it might not be a bad idea for various reasons but at the end of the day we need to be able to build enough homes (and schools and hospitals etc) for our growth. As a nation that's something we HAVE to have.
And we don't. So we're going to have massive problems with rental prices and home prices and availability no matter what else we do, period. The only other answer as noted was a significant and prolonged year after year decrease in population and i don't see that happening shy of a war.