As a Creek, I'm not happy about being on the business end of history (and have no clue what Jackson did to get on the $20), but much of the "genocide" suffered by my people was not intentional.
In the first 50 years after Columbus landed, 90% of the Native American population died off due to a wave of smallpox and flu epidemics. These were by no means designed, and when 17th Century Europeans landed and saw a dying Native people leave seemingly free land (mostly because they did not recognize the concept of land ownership), they assumed that God had awarded them some real estate.
The trouble was the answer. Instead of offering Indians a share of the new country, they considered them foreign powers, so as to more easily acquire land. Instead of honoring treaties, the U.S. government broke them. When they realized that the damage they had done, they devised a system that made them dependent on the government in a reservation system that is justly named. I would have reservations about living in such a place. Medical care, food and housing are free...and worth it. you can get a job, but few businesses invest in such a place (showing both the good and bad parts of the free enterprise system). A Reservation Indian is 40 times more likely to committ suicide than an Indian off.
Any attempt to leave the reservation results in the forfeiture of your lands, leaving the only life you've known, and pratically losing your family (kinda like DFing). Plus, there's little gaurantee of success outside. Most crash and burn soon after leaving, with a barely adequate education (BIA schools) and some culture shock.
I wa lucky. I grew up in Oklahoma, a state without reservations and 15% Native population. I could see examples around me: judges, professors, bank presidents, etc. who were Indian. Not that a person needs examples of their own kind, but when you look around and see everybody who looks like you failing, it really hampers your outlook.
And that concept of "Indian soverignty" that the government endorsed to better extracate the Indians? We use that duplicity now to leverage Indian business and Casinos. We get complaints about it, but hey, they're your rules, you wanted them. Don't hate the playa...hate the game.