Rental income is taxed at 100%, FYI.

I think carrot works better than stick. Instead of punishing everyone who made an investment, and spending god knows how much money to enforce it, just offer a one time capital gains exemption on any investment single family dwelling that has rental income for more than a year. But make that exemption dependent on the sale going to someone who doesn't already own a home. (No landlords scooping up extra properties) this puts sellers in connection with buyers and since the seller is getting a big payout they can do the extra leg work. I bet many of the properties get sold to existing tenants.

The government gets an easy cost effective way to free up supply, and it doesn't actually take money out of their pocket. (Just removes future tax income). Limit the program to no more than 3 years. Anyone who is a casual landlord will jump to get out. Boomers in retirement will jump at it as they will have owned these properties for years. This will free up supply in months, not years. Everyone I know who owns rentals that I discussed this with said they would sell if they could avoid capital gains.

That's my $0.02. FWIW

But then how would we generate GDP?

Your solution focusing on increasing the supply of single family homes is questionable. Single family homes are incapable of supporting affordable housing markets in high demand areas like Toronto, Quebec, Ontario, and Vancouver, which are where most Canadians live. North America needs more flexibility and capital to support upzoning the housing supply we already have from the overused SFH to missing middle multiplexes, or from those to low rise apartments, or from those to 5 over 1 style buildings, or from those to towers. The rigid Euclidean zoning policies of North America mean that even if all housing stock was privately owned by residents, there would still be a shortage in the high demand places where most people live, leading to continued high prices. Especially because we have so much trouble building quality public transit that would open up more land as desirable for development. High speed rail between Windsor and Quebec City could spread out the demand to existing supply in smaller low-cost cities while providing a boon to those cities' economies, but Via Rail has pretty definitively shut that down in favor of HFR at this point for cost reasons

This is the only idea aggressive enough to work which is why they will never let it happen

So what happens to a rental highrise in your policy idea?

So Bob sees your tax, looks at the Ahmed family renting his unit. Says "oh crap, uh, Ahmeds, you're out, I need to put my brother Doug in there to dodge this tax!"

Result: Brother Doug moves from a tiny apartment to living in Bob's house.

The Ahmeds cannot find another place, because half the Bobs are doing a similar scam, and the other half the Bobs are doubling their rents because they can see they now have a good that's in even shorter supply and they don't feel guilty at all for this because they're now paying triple property tax.

The Ahmeds now live in their car and eat cat food.

You know when the number of rentable units goes down, rental prices go up, right? I'm all for going after people who leave units vacant, and for taxing the income people get from these investments, but taxing rental units means making the rent price worse.

Or at the very least, the focus could go into de-commodifying rentals so that everyone always has a fall-back option for safe, clean, affordable places to live even if they can't buy a house/condo. Nobody should be seeking profit in a manner that endangers people's safety.