Maybe if "more people" includes the same people buying more houses. More people getting outbid for one house is kind of the opposite.
Basket of goods makes inflation malleable. So 2018/2019 it got a mallet. Then Treasury and the Fed could've propped up long rates by buying long term/selling short term in 2020 and reduced the RE bubble, inflation, and the illiquidity of golden handcuffs. But POTUS was combover deep in RE debt and needed to refi. So.