There is clearly a shortage of homes for sale but that is an important distinction. Most estimates put the number of vacant single family homes in the US at ~16 million.

Construction has been depressed but so has household formation and household size.

Investors have been buying and building 30%+ of all homes for years until the last few months. There is a reason they are halting investment in mass across the country. There are plenty of homes. There just aren't enough of them for sale to push prices down. Good news for home owners, bad news for landlords and first time buyers in a lot of places.