Canada

While I'm pretty much just guessing that closing the supply gap will on its own force the market to compete rather than pad their margins, the obvious additional step would be having the public developer sell only to individuals/families that own no other property. Even if it isn't feasible to mandate the same for secondary sales, that would still sap rental demand. Plenty of young people (and older generations stuck in a poverty cycle or unable to map a retirement) would choose home ownership over the chance to flip a starter home for profit and then keep renting or gamble on upsizing while forces conspire to cool the market.

I can't recall for sure, but I think at some point Carney specifically mentioned developing small starter homes. That'll sap demand for the larger, more expensive homes that previously had no alternatives, and be a very inefficient property to manage. (Individuals will still speculate if allowed, and their financial blunders would likely add some downward pressure as well, though not as much as reducing rental demand.)

Overall, there certainly are some counterbalancing forces that would prevent housing prices from going down significantly, and I suspect that's also intended or at least included in projections. Carney is still a true blue neoliberal, and he's not looking to upset the asset holding class. I'd wager his target is continued appreciation but at a rate near or below general inflation.

I think you bring up a good point about capital holding back to buy a dip. The answer to that is probably enticing those dollars into other investments around further extraction, new manufacturing, and (maybe) R&D. The last one probably won't draw that much private interest though -- it's too high a risk when the economy isn't booming overall.