It would somewhat. But the systemic rationing of homes by the planning system is the root cause of the shortage and the policy problem.

Building a few more homes under our current system and moving to a new planning system entirely have very different outcomes. https://twitter.com/HenryPryor/status/1301416411156434950

In terms of "what we build and for whom" - the reason we do not do better on that at present is our system cannot. The conditions required for our planning system to achieve efficient outcomes are so demanding that they are impossible to meet. https://twitter.com/AntBreach/status/1273872577254096896?s=19

This is where a lot of property people come a bit stuck. They've observed that historic increases in supply do not seem to have changed things, and are thus sceptical. The economic theory on shortages and planning explains how this can occur though, but it's outside their patch.

Bish bash bosh. Good thread summing up the academic evidence on why housing outcomes are not solely driven by changes in interest rates and credit conditions. https://twitter.com/IronEconomist/status/1301461179278266368?s=19