Just because supply of shelter in certain locales has not kept up with demand for that specific locale, and/or is affected by numerous legalities regarding things like eviction and zoning codes and fire codes and animals, does not mean invalid the theory of higher prices incentivizing sellers to increase supply.
… why would incentivizing supply of staples be a good idea? If I make 2,000,000,000 more eggs you would expect that the vast majority of those would not be consumed, because people already consume staples at a near optimal rate. The sales of substitute goods would go down, but you’d almost certainly expect a rotating set of WICesque price fixing to combat the natural rise in price?