Being part Sami I think it's fascinating to read about the system of reservations in the USA. I'm not sure about minority rule, but I'm clearly in favour of saving the unique cultures and ethnicities from dying out.
After many years of persecution in Northeren Europe—including forced assimilation often called "Norwegianization" or "Swedification," and near extinction in Russia—we've finally gotten some recognition as a nation of our own, at least in the Nordics. We have our own parliament (Sámediggi) and flag, for instance, and enjoy semi-autonomous leadership in "our" historical regions (called Sápmi) in close cooperation with the governments of Finland, Norway and Sweden. As such it acts more like a subset of the respective governments of the Nordics.
Now, both the finnic and germanic populations are also indigenous to the Nordics together with the finno-ugric Samis, so in that sense it's a bit different from the native population of the USA, where the other nations are almost all of immigrant descent. On the other hand, just like the Native Americans, Samis are in the clear minority in Northeren Europe, with only about 100.000 members, some of whom can't even speak their own language due to the assimilation policies (like me, although I do know a few words). Thus our culture and unique way of life is indeed in danger of extinction. For that reason alone I think it's important to at least recognize the ethnicity, and perhaps save it from the "tooth of time" as it were. Perhaps especially since most Samis today enjoy a modern lifestyle, and only very few live the traditional nomadic lifestyle of reindeer herding. If I'm not mistaken, the same is true for the Native Americans. In any case I'm happy we can finally enjoy peace and democracy with one another.
All the best, from Norway! <3