Canada

It really wouldn't.

A) It prevents renting at all except for basement suites. So no more rental buildings, which make up the majority of rentals available. Renting is an important housing option, as not everyone wants to own, nor should they have to. Move to a city to go to university, and you have to buy a house just to live in for 2-4 years before you have to sell it to move elsewhere for a job? Have a job that requires you go somewhere else for a few months while you , too bad hotel for 6 months instead of being able to rent an apartment.

B) If you do the math and even take out dedicated rental buildings, there really aren't that many homes that are owned as a second place. It's about 15% of the total market, and a large chunk of that are cottages and lake houses away from the cities where people actually want to live.

The big place/small place issue is actually more of a problem than the the double ownership you're talking about. There are more total bedrooms in Canada than there are people, and once you account for couples usually sharing a bedroom, there's actually a ton of extra bedrooms across the country. The problem is that they're not distributed properly across the population, 4+ bedroom family homes that were bought to raise children are being kept for decades by empty-nest couples who don't want to downsize.