A socialized housing market replaces exorbitant prices with a lottery; public-subsidized housing in Stockholm has a waiting list of years. The way to stabilize the demand curve is to increase to supply.
Socialized housing is a management technique. It does not inherently create housing. Read about Stockholm's situation if you are interested in learning about the topic.
It is indisputable that there have been successful socialized housing schemes. It is also indisputable there are successful free-market housing systems; for example, Minneapolis.
A vanishingly small portion of the US rental market is rent controlled - fractions of one percent. In New York City there are only about 25,000 units that are actually rent controlled - tenants who have lived continuously since July 1, 1971 in a building built before 1947.
Rent stabilization - caps on how much landlords are permitted to increase rent - are also not that widespread. Washington DC is unusual in having over half of its rental stock covered by rent stabilization, but even in NYC less than half of the rental stock has stabilized rents.
Apparently that is beyond the high and mighty Federal Reserve employees who wrote this speculation.
The housing market needs to be socialized.