Well, don't forget that there are quite a few instances where European nations or governments worked together against outside threats. For example when the Polish and others helped defend Vienna against the Ottomans and so on. I agree that a full unification is desirable though.
And as for the whole conquering thing, it's laughable because the American settlers faced technologically inferior Native Americans while the European powers were mostly on the same level. Siberia is mostly empty space, not hard to conquer but also not very useful for settling and food production. And settling more people in the Nevada desert will eat up a lot of resources, probably more than you can get from the desert. In the same way many of the European conquests for colonies were against inferior enemies.
A better question may be why European warfare was superior to that of many other nations or tribes around the world? And maybe that was because of all the fighting between equal nations and a strive to improve one's own weaponry, which then inevitably spread to other factions, maintaining the power balance within Europe, but also raising the war tech above that of other people around the world. And then all the misery also brought up all these ideas of how to get peace that led to enlightenment etc.
Americans just built on this advantage the Europeans had acquired to conquer their territory against inferior enemies. In the modern day and age, I'd argue it's more useful to work together than against one another however. And it's somewhat weird to say that Europe has missed that trend because the EU still exists. The small guy may not support it but the small guy in America is hoarding assault rifles to bring down the federal government one day so there's not that much of a difference...
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