Do we have a shortage? Or changes in lifestyle? 50,60,70 years ago extended families lived together. Now Grandparents , Parents, and Adult Children all have their own place. The adult children don't want to live together so they all have their own place. This leads to the number of households created. It does not have a lot to do with birth rate, it is the number of house holds. I believe this is why I believe many immigrant families continue to move to the US and do well. They live together in one house. Imagine how quickly the "typical' U.S. family could own a home with no debt if three generations lived together and paid one home off instead of renting three?
I also question how many new units we need. Lifestyle creep has led us to build very large homes. New homes in my area are often 2,500 to 3,000 sq ft and they are for a family of 3 or 4. Eventually these children will move out and there will be only one or two adults in the home. We def have some McMansions that could be remodeled to add a second unit and this would save infrastructure costs.
After World War 2, houses were built at about 800 sq feet. When families had enough money they remodeled the attic or basement. I think a lot of folks would be better off if there were more homes litke this being built today. Maybe smaller homes with an ADU.