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.