Why was it important for white Americans to assume that Indians were a single cultural mass of primitive people with no history before the coming of whites? How did this help justify expropriating their lands?
It was important for white Americans to believe these things about the Native Americans because it helped to justify treating them poorly and taking away their land.
The most important aspect of this set of ideas about Native Americans was the idea that they were primitive and savage. This meant that they did not really deserve to be treated as regular human beings with the rights that regular human beings deserve to have. Since they were savages, they could be treated brutally. Since they were primitive and were not really using (from the European perspective) their lands, they had no real right to those lands.
The idea that the Native Americans had no real history also made it more acceptable to evict them violently. It meant that they did not really have a strong claim on the lands that they occupied. The idea of the Native Americans as an undifferentiated mass was also somewhat important. It allowed the white Americans to treat them all the same without having to exert the effort to determine which nations ought to be treated better because they were in some way more “civilized” by European and American standards.