Trying to cool the market isn't going to reduce the need. When vacancies for residential rental properties are sitting at 5% or less for just about every major city in Canada, residents are seeing one of two options: pay more than you want to for a house or pay more than you want to for a rental unit. The demand isn't going away, so the only options are to increase the supply or reduce the capacity for people to buy personal residences.
It would barely be a start, and would actively hurt the people you remove from the housing market. We already have places where, in spite of the ridiculous prices, it can be cheaper to own than it is to rent. Now you propose that raising the barrier to own is both not going to affect those who can least afford an increase in housing costs and not going to raise the cost to rent?
Proposals that raise the bar for buyers of primary residences aren't the way to go. Raising the bar on additional residences is the target you want to look at. It will remove buyers from the market which will reduce the pressure on purchasers of primary residences.
Best to plug the hole in the boat before you start bailing.
New stock coming on the market is being bought up by investors at record levels.
Heaven forbid we follow other countries leads and just have heft graduated taxes beyond primary residences (like Singapore). But we wouldn't want to lose the wealthy landlord vote now would we?
The original post mentioned removing incentives for people buying or selling primary residences, which has almost nothing to do with the housing crisis.