The entire point of the EU as an entity is that it allows people to move everywhere that companies and services can move to.
Additionally, the entire problem of the refugee crisis was that countries controlled their own border – and everyone refused to do anything, instead telling Greece to prevent them from entering, and Greece said they’d just open their borders. In fact, the EU only got control of the borders in September 2016! http://www.consilium.europa.eu/en/press/press-releases/2016/...