Why pay 40% market value?
How about this instead. If we continue to have rent and landlords, let's make a market incentive to lower prices.
Tax empty housing at a rate proportional to the advertised rental rate. Example, if a landlord has an unused unit listed for 1500 a month, they pay an empty housing penalty of, let's arbitrarily say 20%. Now they have an incentive to fill the unit at a lower price. They can no longer just price-gouge with their competitors to drive up rates. What do we do with the money we receive from those penalties? We provide housing assistance. So now the top and the bottom of the market start to balance each other out. Here's the real cool thing about this system, you can tie that penalty rate to the number of housing-insecure or unhoused people in the population. Now we can have a self-regulating system that provides an incentive to push rental rates down, but also gives low-income renters more money to rent with.