Is it better in neighboring countries?. There was a discussion [1] about controlled rent market few days ago, it seems that the problem is related to growth.
I think EU citizens have the right to live anywhere in the EU, so while not exactly the same as the US due to language and cultural differences, it might still have a noticeable effect. But I am not well versed in the topic, so I would only be able to guess.
[1] https://www.bbc.com/news/business-58317555