The first best solution isn’t to reduce the cost of rents, its to increase wage rates. You increase the wage rates by removing subsidy programs to the working poor that induce them to accept lower paying jobs. Subsidies to low income earners are nothing more than a way to suppress their wages as businesses no longer have to pay workers a wage to cover their COL as the taxpayer foots the bill for the difference. In effect, welfare spending is nothing more than a way to keep the cost of employment low, which lowers prices, but means increased taxes to make up the difference. Quit subsidizing businesses and wage earners through government programs and slowly the problem will solve itself. Low wage workers will migrate to more affordable areas, the supply of low wage workers will decrease, and wages will rise, along with prices to pay them. Now you have a market. Rather than high income earners being expropriated to fund the programs that subsidize the low wages, the prices will increase to close the gap subsidization once filled.
Or, we can continue business as usual, use rent controls that will always fail, and increase taxes on less than half the working population to pay for the gap in the wages the programs induce. Granted, you’re not going to stay in office if you suggest a real solution to the problem, when you remove programs like this, you reduce your ability to buy votes.