If you don't use price to determine who receives a scarce good, then you're stuck with other bad mechanisms. In Stockholm, for example, waiting lists for apartments can be over a decade long.
Much better to recognize that "The problem is not that there isn't sufficient housing" is wrong and legalize building more housing.
What's wrong with waiting lists? Sounds much fairer than to give all housing to rich folks. I'm not advocating that 100% of housing should be run this way, but for sure more than what is now (in most large EU cities).
I'm not saying social housing is bad. We should definitely have more social housing.
I am saying "The problem is not that there isn't sufficient housing" is wrong. Very very very wrong. There are massive supply shortages of housing in many many places. Governments need to fix their oppressive zoning policies so they stop preventing people from living where they want to live (either because of $, because of waiting lists, or any other mechanism).
That's what people say until they are on the shitty end of the deal. The distorted housing markets in Germany are pretty rough for newcomers -- think immigrants (not a minority group, refugee, etc), international students, seasonal workers...
Those people either don't know enough about the system to take advantage of it, or don't have enough time to wait in waiting lists, so they end up paying twice what their native peers pay. But hey, they don't have a vote anyway, so it's all good...