I know how implementation in national legislation of EU policies and directives is *supposed* to work, but the reality is that it doesn't and is not likely to with the current construct.
You can choose virtually any topic and compare the legislation in different countries and you will discover that the variation of the content of it is substantial. After that comes the method of implementation and policing and finally what happens on the ground. The different styles and cultures make sure of that.
The U.S. hasn't achieved the kind of uniformity that you describe and they have a federal system and have has a considerably longer period to make it happen had they wanted to do so.
Sorry, but the situation you describe is not really wanted by people if they think that it will interfere with their lives. If they live in an environment where the law is more a matter of policy then they probably don't care. This is all stuff promoted by those seeking to gain power over others because they are unable to do a proper day's work.
It's a dream, and rather a wet one.