I disagree with this statement, cheap credit allows banks to offer longer term mortgages and buyers able to afford a larger principal with the same per-month cost, pushing the prices upwards due to keeping payments low on a per-month basis, due to low interests and longer term plans.
This definitely pushes the price of all market upwards. It's a similar effect to tuition costs in the US, cheap credit, bankruptcy laws make them pretty safe for banks to take risk, flooding the market and allowing universities to hike prices.
Building is fundamental, but cheap credit has an upwards pressure in price, magnifying the effect.
All in all, I completely agree with your take on the solution. Build fucking more, population and specially cities have grown quite a lot on the past 3-4 decades, we still live with most dwellings built then than now.