> The US is and always has been a country of immigrants
Settlers founding new places are different from immigrants. The US was created by British settlers. Its language, laws, political system, and to a great extent its culture are British. If you look at various statistics, the Anglo countries share strong commonalities, even though people of British descent are now a distinct minority in the US (while being a majority in Britain, Canada, and Australia).
Over time, other people moved in. Those were immigrants. But for a long time it wasn’t immigration as we know it today. Many of them created greenfield communities, settling large swaths of the Midwest, etc. Those communities were pockets of Germans, etc., in a country that was still distinctly British.
“Immigration” since the 20th century looks quite different again. Immigrants aren’t founding new greenfield communities, they are moving into (and changing) existing ones. The place where I grew up is culturally unrecognizable now thanks to immigration (both of foreigners and of people from other parts of the country).