Would arguably reduce housing costs on average?

(Canadian here with some knowledge of the industry)

It hasn’t reduced prices on average, but it does flatten out the distribution across the country. I would say that for small towns the short-term effect has been overall negative, because it drives up housing prices in regions that historically have lower wages, and also ties up the construction industry and drives up prices there as well, so it becomes more difficult to both buy an existing house and build a new one. The real winners in the equation are the remote workers who are no longer tied to big cities and can use their “big city money” to buy pretty much whatever they want in a small town.

Long-term (after things have stabilized, maybe a decade, and assuming the “immigrants” stick around) it will be more positive, because the small towns’ tax base and demographics will be rejuvenated. Short term infrastructure pains are real though.