Definitely a problem in Canada, but fortunately our government seemingly follows OP's ridiculous logic, and plans to continue increasing our population by 1.3% every year, via an aggressive immigration push. Never mind ensuring we have housing for them or anything.
Not only are cities in America not overcrowded, almost all of them are extremely low density sprawl. There is like 1 city in America with a respectable level of density. The average American city would be much nicer and much more livable if they quadrupled the number of people living there.
Hypothetically more of these cities could start to build out subway, light rail, heavy rail networks; which would support higher density. But American cities don't seem to be capable of that. Maybe it's a lack of money, maybe a lack of political will, maybe it's American car culture. But it's irrelevant. It takes a really long time to build out that infrastructure, and in the meantime, the city has the infrastructure that it has, which is insufficient for keeping both housing costs and commuting times down.