I have been reading a book called Empires of Trust by Thomas F. Madden and he proposed this very scenario in his book. In the book, he compares America's European allies (who have turned to the United States to protect them militarily and prevent them from going to war with one another by acting as an outside power uninterested in territorial gain) to Rome's Latin allies from the Italian peninsula. Rome's Latin allies eventually realized that all important decisions affecting them were not being made by their local governments but by the Senate at Rome and so they demanded the right to be Romans themselves, foremost they demanded the right to vote. Rome resisted this demand which led to the Social War from 91 B.C. to 88 B.C. after which Rome conceded citizenship and suffrage to all citizens of its Latin allies.
I doubt that many, if any, would argue that the most important decisions affecting Europe (specifically Western Europe) are not made in the halls of Congress and in the White House. Since this has become the case and the Europeans are, over time, becoming de facto provinces of the United States, that leads to one very important question: should Europeans be allowed to vote in federal elections?