It is possible for regulation to lower the cost of some things. For example, currently the regulatory environment in many California real estate market lowers the cost of holding rental property. In a more competitive, less regulated market, the opportunity cost of buildin developing now housing would be lower, so landlords would have more cost (indirectly through decreased rent or directly through more frequent renovations).

Hopefully this move leads relaxed zoning laws and regulations, allowing new development... People who want such things will gain political clout because capital will want return on investment, and rent control shifts the calculus for good ROI in the real estate market toward new development (marginally).

I'm sure hundreds of economists have written thousands of papers about this subject, each going its own idiosyncratic way, so maybe I've actually been proven wrong in this particular case, I don't know, but I have to say that the idea that regulation only ever increases costs is silly.