I don't know about restricting rent but they certainly had a progressive tax on high rents, a 1% income tax to fund housing, and then used that to build a ton of high quality social housing with balconies and amenities for all. I also like to think it helped that they slapped a big sign on each to proudly let people know it was their tax dollars at work.

I didn't stay in social housing while I living there but I never once heard people complain about it. They basically just didn't think much about it at all and felt it was a good system and then would ask me why the US only makes it for poor people.