That has almost nothing to do with the EU and almost everything to do with NATO, the massive number of US troops (they outnumber all European troops in Europe),

That has almost nothing to do with the EU and almost everything to do with NATO, the massive number of US troops (they outnumber all European troops in Europe), nuclear deterrents, and shared foreign policy goals (i.e. managing the rise of China, combating terrorism, and deterring Russian meddling).