No, this is not how this works. Rent is set by demand and (very insufficient) supply.
If landlord could increase rent by $X - they would have increased it already (software in TFA speeds up the process, but doesn't set market clearing price). A simple thought experiment would be something akin "98% tax on rental income". "Pass it to renter" would imply 50x increase in rent to preserve existing income.
Bottom line: make it easier to build more housing. it doesn't have to be subsidized/affordable/below market rate[0]. Any addition of units has downward effect on rent across all range of prices.
[0] > [In Helsinki] The supply of new market rate units triggers moving chains that quickly reach middle- and low-income neighborhoods and individuals. Thus, new market-rate construction loosens the housing market in middle- and low-income areas even in the short run.
From "City-wide effects of new housing supply: Evidence from moving chains" https://ideas.repec.org/p/fer/wpaper/146.html