Americans on average are too stupid and too easily manipulated for this to ever be a matter of concern for them though.
And women have been able to vote in the U.S. for decades longer than the governments of the E.U.'s largest countries (France, Germany, Spain, and Italy) have existed in their current democratic forms. When women got the right to vote in Wyoming, kicking off the movement towards national women's suffrage, the French were on Napoleon III, Spain had a king, Germany wasn't even a country yet, and Italy was a recently unified Kingdom.