These are the capstone of the United States and Canada's relations with Native Americans, which are still considered "independent" nations within the territory. This affects things like law enforcement on the reservations these countries have set aside for Native Americans, which is why a certain Mohawk Indian drug trafficker on the border between the US and Canada was able to build his notoriety and become one of the major drug traffickers in North America--corruption of local law enforcement and a certain legal interpretation of treaties signed with the Mohawk Nation.
So what if both Britain and its successor the United States decided to dispense with the idea of American Indians as sovereign nations? Australia and its Aboriginals might be a good example, since very, very few treaties were ever signed and Australia treated their natives far different than the US treated ours.
Essentially, treating the natives as anyone else, which in pre-20th terms, means subjecting them to discrimination and other junk if the US tries to incorporate them. The "Five Civilised Tribes" being important landowners in the US South might be something to look up to, even if for the non-wealthy Cherokee, Creek, etc. it certainly wasn't good as the aristocracy of the tribe had become. No Indian Removal might be a result, as anyone in the South who wanted cheap labour but didn't have slaves available could use poor Cherokee or otherwise.
This would extend into other American Indian groups, but in more difficult ways. It's hard to incorporate steppe nomads like the Sioux and Comanche. The US might hit them even harder than OTL. But without a precedence for a treaty, might these groups surrender earlier once they realise the US will keep murdering all their women and children and never stop at trying to destroy them? Not that their isn't a potential for peace as early as the American Civil War, if the US wants to keep what their vision was for 19th century Indian affairs (pretty solid if a bit misguided, ruined by lack of funding and plenty of idiots on the American side, but ultimately not malignant?).