No, it's overstrained because every major metro area in the US has policies in place that keep enough housing from being built. Housing would need to be built at literally twice the current rate just to cover the current deficit of housing compared to number of families in a reasonable timeframe [1].
Cash just means no financing contingency. Some sellers don't ask for proof of funds. People were risking their deposits on the possibility that they may not get financing, others had outright cash. Both fell into the same statistic here.
It seems like the western world has the exact opposite housing policy to China.
China has completely built out cities just waiting for hundreds of millions of people to move in, but we enrich boomers by subsisting and effectively subsidizing mortgages from the same suburbs built in the 60s and 70s.