Three millenia? MILLENIA? Not a single European country existed three millenia ago.
Three millenia ago you'd have to go further East.
The British used the American penal colonies chiefly for lumber, having run low on availability in Europe. Navies and merchant shipping require lumber. The cleared ground was then used for farming. Other than that, the colonies did what again? Oh, almost forgot that Earth shaking beaver pelt industry, also almost wiped out in Europe. Golly.
The fortunes of European countries have been fading since what again? Which countries had booms in the last HALF millenia? Why?
That's right, you got it, those that became prosperous did so by plundering elsewhere. Portugal, Spain, France, Britain. Resource availability in colonies declines, so does the market dependent on them, so does their prominence on the world stage.
Spain as the most powerful and richest nation coinciding with its encounter and colonization of the Americas was not accidental. It's current status as a has been is likewise not accidental. France is a joke, and even funnier is Portugal, once master of the World - again, not coincidentally coinciding when it realized Africa extended further south than the Sahara and that Asia waited on the other side of that continent.
Westward expansion in the US found not just more timber, but silver, gold, oil. If we had not stolen half of Mexico, we would not have acquired those commodities, and thus would not have been able to profit from them. Welcome to capitalism. Demand is irrelevent without supply. Early on the USA didn't even have enough precious metals to make sufficient coins for use. The US Dollar - down the concept of the Quarter - is based on the Mexican Peso, not the British Pound, know why? That was the money we used here.
Yes, back to the motherland, Britain. In the space of a generation they went from the greatest empire the world had ever seen to the 51st of United States. Have a clue why? Lost its colonies, lost its bucket of pixie dust.
Like to use your Google Calculate App to figure out which Federation in the Americas has been in decline since the 1950s? Dependent on a gluttonous consumer base, and the import of aliens for cheap labor and economic growth - responsible for 70% of all small business starts - as well as brains - science, med, tech research and development carried out by people from the Middle East, India, East Asia, Africa, etc because people like you are too busy taking selfies at Walmart.