You are correct, all of this benefit would end up being taken by landlords due to their ability to dictate prices - btw government subsidized housing can be a different situation and the government can be an intentionally inefficient market actor to benefit the renters. I think there are still more accurate way to subsidize the lower class though, a reduced income tax is more likely to directly translate into a higher savings rate and more consumer power - and that last bit benefits us all by increasing the velocity of money.

Would be an incentive for the city or state to enact policies for making housing more affordable. From what I've seen a lot of housing issues are coming from not-in-my-backyard-ism and zoning.