This article has a bunch of cringeworthy prose, but has some worthwhile graphs of data showing that price-fixing isn't the answer:
https://www.bloomberg.com/opinion/articles/2021-03-02/berlin...
See also numerous Planet Money stories about rent control:
https://www.npr.org/sections/money/2019/03/05/700432258/the-...
https://www.npr.org/2022/01/31/1077086398/is-it-time-to-cont...
https://www.npr.org/2019/03/29/707908952/the-evidence-agains...
Note that even very-progressive Jerusalem Demsas was once against rent control and has only switched sides as a palliative measure because fixing the root cause of the problem is proving too difficult.
Freakonomics also did a show on the topic:
https://freakonomics.com/podcast/why-rent-control-doesnt-wor...