That was my first thought too, but our system also depends on powers being divided in appropriate ways, and an orderly election schedule. The Europeans don't have a history of either of those (particularly the latter).
The only problem with the EU is that the solution already exists... and the Americans invented it.
Europeans do NOT understand that the “United States” began as a solution to the same problem that Europe now faces: separate, autonomous states coming together to form a union.
The articles of confederation showed how NOT to create a true federal system.
Fortunately our founding fathers didn’t have a “Great Satan” as a bugaboo and could modify the articles into a constitution.
If Europeans could get over their Ameriphobia for 10 minutes, they’d see the wisdom...