The gov subsidizing rentee's housing payments to existing landlords en masse is the landlords' wet dreams. Not only do they get to capture the income of the rentee's, but also their tax dollars! The fundamental bargaining position will remain unchanged!

Before you say "that's why the gov should build the housing", it's important to remember that centrally planned things are generally worse than market planned ones, it's a bitter lesson but history shows it time and time again. Instead of rentees choosing how to spend their money the gov, who only cares in an indirect way, will be making that decision for them. Inevitably someone in this compulsory taxation-gov-built-housing loop will realize their bargaining position and create insurmountable corruption. What would a rentee do, swap local govs to pay taxes to in their city?

If you want your gov to help your situation, use the gov to allow people to build more housing. If that's not an option, you gotta start new somewhere else.