Hi back in the 70's and early 80's there were many Bible prophecy teachers who taught what you are suggesting as the rebuilt Roman empire is seen in Daniel as being the 10 kings and the EU was supposed to ascend while the US would be in decline. This view is not correct and I can demonstrate why.
The infrastructure for global government is the UN and not the EU. If you study globalization the EU is going to be 1 of 10 heads as the world is to be divided into 10 such regions. The UN is expanding its power with the use of the World Bank and the IMF and when the dollar era is over the IMF will issue global fiat money to the world. The globalist in the US ,Europe Australia, China, the Vatican and all are putting all the goals of the UN plan Agenda 21 and its newer version Millinnium 2 into treaties which become national laws which give the UN an ever rising stake in their governments. In 2000 the UN had Michael Gorbachev write a document called the Earth Charter which was placed in a new ark of the covenant and carried with poles 300 miles and placed in the UN building after 9/11. This is symbolically the new commandments from God for the whole earth. Outside the UN building is the Bible verse they shall beat their swords into plowshares and the spears into pruning hooks and they shall learn war no more. This again is attributing a verse about Jesus mission to the UN. The global central banks and secret societies are all working for this specific end which will be the seat of power the antichrist takes.
The teaching in the 70's and 80's saw the EU rising as a Super Power and being stronger than the US ever was but his si not true and the EU is in huge financial trouble as are all the nations. If the EU goes down to 10 it will have much less power than it does now and it will not be able to take over control of the whole world.
I hear what you are saying about the 1980's and Jack Van Impe for example saying Juan Carlos as the Antichrist based upon Spain becoming the 11th EU nation.
However, Brian, not ten world regions because near the end of the 7 years, the world powers from the four directions of the compass converge in the middle east in Daniel 11:40-45.
The fourth kingdom that the ten kings come out from is the end time Roman Empire - or else it would have given as a fifth kingdom.
It is not until the last 42 months of the 7 years that the fourth empire becomes dominant over the other nations of the earth, exerting its will and influence over the other nations. To be challenged right near the end of the seven years.
Not that all nations will be members of the fourth empire. Can't be, otherwise we cannot have in Daniel 11:40-45, the kings of north, south, west (implied), and news from the east - the kings of the east marching in Revelation 16:12.
Before the 7 years begin, and the next thing of the prophecy timeline, regarding the establishment of the ten kings, out of which, the little horn will become leader of the EU before Gog/Magog attacks and will head toward Israel with a strong army from a location north and west of Israel (Daniel 8:9) - from one of the four Alexander break up kingdoms - specifically Greece in our times. Greece will be just the staging and massing of his EU forces location.
The end times are a fluid progression of events. The little horn person for example does not immediately equate to being the Antichrist. He does not become the Antichrist until after he becomes the King of Israel, anointed so by the Jews who will believe that he is the messiah following Gog/Magog.
And he will only be the Antichrist for about 3 years 3 months, before becoming the beast of Revelation, who the whole world - except for the saints - will worship.
The ten kings and seven kings of Revelation 17 are of the fourth kingdom. Six of the seven kings are historic being - Julius Caesar, Augustus Caesar, Tiberius, Caligula, Claudius, Nero. King seven will be the end times little horn person, descended from that family line, the Julio-Claudians.
The ten kings are end times leaders of the EU, the end times version of the Roman Empire.
After the little horn, at first the leader of the EU, goes through the stages of becoming the Antichrist King of Israel, then as the revealed man of sin (ending his time as the Antichrist), and ultimately becoming the beast who the world will worship as God (except for the saints) - will be the eighth king of the Roman Empire (after being killed and brought back to life).
As the EU will become the dominant world power over the rest of the world with him having all of their military power at his disposal. The United States and Canada will most likely be aligned with his power base with him being the King of the West for the final convergence into the middle east right before the sixth seal takes place.
Then the focus will change to all of the kings of the earth uniting their armies in Revelation 16:16 to fight Jesus in hope of avoiding the wrath of his judgment on them.