Really what you are describing is a superstate akin to the US Federal Government, which is not the purpose or goal of the union.
Countries within the EU also have vastly different cultural attitudes to many issues. For example, in some countries having a national ID card is mandatory (Germany) and others don't have a national ID card at all (Ireland). Some countries have opted-out of the Euro single currency (Denmark) and others are dragging their heels even though they have an obligation to join (Sweden, Hungary, Poland, etc). Some countries have opted-out of the EU Mutual Defence Clause. One (Ireland again, due to border issues with Northern Ireland) didn't join Schengen.
Trying to force such a diverse set of populations into a single superstate will just lead to the break up of the union.