It's the other way round:) Europe is salivating at the American real estate market. Some European countries don't have capital gains tax on real estate and real estate is the only investment vehicle without this tax. The only country where real estate prices haven't skyrocket looks to be Finland but their general situation is very specific and it's hard to say whether it's by design or by accident.

Social housing in Europe while exists, distribution of it is extremely corrupted process. Applying and waiting will give you something in 5 years or never, you'll know in 5 years. You have to be young couple both employed with perfect portfolio, or whatever the role model in that time and location is. Young couples both employed in desirable city basically don't exist anymore, even if you are after two rounds of waiting suddenly you are not a young couple anymore:) Usually you have to know someone and give a bribe.