But I think this needs much more priority than the 'one market' benefits for big business they're working on. It's really a mess if you move around in the EU now, it's not at all like in America.
They should fix the voting too: Right now as an expat I can only vote for my home country which has zero bearing on the country I live in :/ And changing nationalities takes 10+ years.
For other stuff like health I don't mind as much (especially as Spain has a much better state health system than the Netherlands' privatised crap :) )
About cooperation between countries; At least the gears are turning, even if it is not somethings that is high on the political agenda. The biggest issue is to have a central database that maps one identity in one country to another. We have not even figured out Inter-country Electronic IDs (via EIDAS) yet, there is no way to even do a manual match of identities between countries using eID. That makes it impossible for you to log on and check your pensions if you work in the wrong country.