It is impossible to analyze the EU without the context of the US. The EU exists because the US allows it to, which wasn't at all obvious in the beginning.
It has been popular lately to complain about European states military spending, which is more than just naive given that NATO decides what can exist and an alternative to NATO would be unrealistic, especially in the shorter term.
If the EU really threatened the US in any manner, that situation would be rectified in a heartbeat. That may sound violent, but it mostly isn't. A lot of it is just the free market at play, but it is a market in harmony with US interests.