Moving across Europe may be harder than moving across the US. But moving across Europe (at least the EU) today is much easier than it was 40 years ago, pre-EU.
The EU is an absolute joke and a bureaucrauts' dream, no wonder our economy shrunk to half the USA's in the last 10 years.
We were told you could easily move to another country. The fact is that in some case you can and in others you cant.
So on that front, the promise of freedom of movement is if not broken one not reality either.