Ok, yeah, no they didn't do that in Europe or anywhere else in the world for that matter. So why just the US (and Canada)? I include Canada because the same things happened there that happened in the US.
Because the First Nations weren't economically exploitable - not on the large-scale.
What I mean is - when Great Britain took over, say.....India or Palestine. India
had money, before the British got there. Palestine, had money. Indonesia had money. These nations already had industry and mass-agriculture. Much like Alexander (as you mentioned), the British could install a small administrative body to run those countries and accept the money, but largely leave the people to continue as before using those countries' own already-existing infrastructure....so they could continue to produce those goods and the money, which of course the British could then take.
Native Americans, at least the ones on the eastern seaboard first encountered by the British - they didn't have money, or an industrial or agricultural product that was relevant to British interests. They DID farm - they produced lots of corn and tobacco, but at the time of contact these crops were unknown in the rest of the world and there wasn't a market for them yet. There was the idea of slaving, and the Spanish certainly gave that a shot in the Americas; but while the British colonists dabbled a bit, it turned out that on the large they didn't really have the stomach for the "work" of it, preferring mostly to just buy slaves from the Dutch who were already doing that "work" in Africa.
What I'm trying to say is, although I hate even putting it this way, but unlike the indigenous peoples of other colonized lands the Native Americans as a population weren't "useful" to the colonial powers. The land itself was far more valuable to them, so the indigenous nations were an inconvenience that needed to be pushed out of the way so they could put Europeans on it who would "properly" develop it to its full potential.
Sadly it wasn't just North America that this happened in, either. The indigenous people of Australia also didn't have anything to offer the colonial powers, and were pushed out of their lands in the same kind of way.