It costs money to hold on to a unit of housing. Supply is increasing (that's the premise; nobody is proposing a one-time increase in supply). How does the investor profit?
If a small number of landlords continue to control the supply (which I understand to also be part of the premise) then they can charge whatever rate allows them to profit. Housing is pretty inelastic and is a first order priority for most people, so they will pay the maximum they can afford if they have to. At least near me, most of the housing being created is owned by large corporations like the Irvine Company, it’s not individual owned.
The investor profits from the appreciation of the property - they may Airbnb in the meantime also. Especially, often the speculator will fix-up the property for a sale - and then the next buyer fixes it up as well. Eventually it be a vacation home or someone might even buy it but the entire process keep a lot of property off the rental market and that increases rents.