Do Turks in other states all assimilate? usually not. In fact in Greece Erdogan complains about Greece not officially recognizing Turks while in the next breath he doesn’t recognize tens of millions of Kurds in Turkey.
My own stance on minorities… I oppose state sponsered multiculturalism but it is not morally obligatory to assimilate. However if one wants to be part of any nation one should participate not cause problems. Learn the language. Have friendly relations with neighbors, Contribute to the economy. And so on. Otherwise the minority should leave for what they see as their homeland. The problem for Kurds is they have no homeland to go to.