"economic area" is not the same as being a sovereign nation. And the EU is not a nation.
It may be someday, and I think the world will be a better place when it happens. But it has not happened yet. And until it does, flying from Italy to France will not be the same as flying from Florida to California.
In the meantime there is no historic basis to pick and chose between the obligations and rights that come from nationhood; it is a package deal.