I don’t think local government contradicts freedom of movement. It seems to me that both is possible, with little federal oversight. The biggest problem is inequality – the EU is perfectly happy to open the borders between its very similar member states but will vigorously protect its outer border.
It's not really about freedom of movement and I guess it's only applicable in representative government. But if you have a federal representative thousands of miles away in DC that has 5 million constituents and a state representative dozens of miles away at the state capitol with 50,000 constituents, you're going to have a lot more impact with the state representative.
The USA is basically the same idea as the EU, it is just supposed to be the international face of our amalgamation of nearby states that have formed an alliance for their mutual protection and simplification. The real laws (i.e. not treaties or other international matters) are supposed to be implemented at the state level or lower.
