Supply and demand have basically no weight in the housing market, lots of capitalist countries have more empty homes than they have homeless people. Once landlords and mortgage banks form a cartel, it becomes only about fleecing the working class that can’t live healthy lives without a roof.

What you describe there is actually a good example of escalation, where a good reform has some negative effects simply because real estate bourgeois types still want to keep profits. If people using the capped price to rent illegally is a systemic issue, then the next step is to curb ownership of multiple homes. If working with reform, every reform should usually be the stepping stone for the next one, and the blame should not fall on the reform itself if the ones causing issues are the same capitalists who made it necessary in the first place.