"Shit Americans say"
The EU is NOTHING like the US. The difference between each member is the same as the difference between the US and Mexico, not like the difference between California and Utah.
It's utter ignorance to suggest that the EU could one day become a single country.
I am European first and foremost, I have an ethnic nationality which is secondary and almost irrelevant. In my mind Euorpe is actual a large collection of regions, which hold more meaning for inhabitants than nation states. But we all love our European brethren no matter who they are.
But in my experience there definitely are Europeans with that view. WW2 left some deep impressions about the dangers of nationalism, especially in Germany. That led some to consider themselves Europeans first.
What we do need is doing more things on the EU level. E.g. there’s no point in all member states building a nuclear umbrella or a space program. Some taxes also work better on an EU level because capital flows freely in the union and makes taxation hard for individual members.
Also, the general area was basically at war most of the time from the Etruscan era to the formation of the EU, and the EU is (amongst other things) an attempt to be at peace, so it would already be a similarity even without repetition.