From an outside perspective though, (one example) isn't the immigration and refugee situation with lack of assimilation becoming a big issue that is forced down each EU member's throat without recourse?
It just seems to me that each country is different and faces different challenges so the EU "prescribing" the same medicine across the board for all countries would not be a good thing. I would compare it to the US federal government passing blanket laws for all US states when really they should be handled by each individual state, as different states have completely different challenges.
Freedom of movement within the EU is part and parcel of being in the single market. Thats already very clear, economically is pretty much undoubtable we will suffer without single market access, or freedom of movement.
Anti immigration sentiment is largely due to some kind of notion that immigrants are simultaneously stealing everyones jobs and everyones benefits. But actually all research points to immigration have a net economic benefit, and that immigrants are far less likely to claim benefits and far more likely to pay into social systems.
The lack of assimilation is nothing to do with the EU, thats each countries responsibility to handle, and additionally the EU does not prescribe levels of the amount of refugees that should be accepted into countries without discussion and vote from all the Union members either.