They tried this in NZ too; it did nothing. Canada - Like New Zealand, and like Australia - relies on simply increasing the population through mass migration to "grow" the economy. This benefits enough powerful people that it will never stop for the sake of mere renters.
Western countries are all trying to encourage immigration because without it their populations will collapse. Right now populations are rising and causing house prices to rise but soon boomers will start dying leaving huge numbers of homes empty.
Global population will peak this century. Birth rates are dropping everywhere, and yes this includes the developing world (West Africa is half what it was, India is below replacement rate). The pool of working age immigrants will grow smaller and smaller. How much longer will we kick this can down the road?
For very long. As long as a country is a more desirable place to live, it will continue to get immigrants. It doesn't matter whether the source country has a growing or shrinking population.
