Most of the land taken east of the Mississippi was done as the result of native tribes siding with the wrong nation in European wars. They saw potential profit and territorial gain from doing so and when they lost with their European allies, they got smacked down for it. Nothing new there. That was standard practice at the time. No ethnic cleansing involved.
Sure, the Cherokee got absolutely screwed, but they are more an exception than the rule.
Other tribes like the Seminole, and later Apache and Modoc, brought it on themselves by being very violent and warlike. Nobody liked that and those tribes got smacked down hard for it.