There are not, and never were, "Indian Princesses". The Indians would be the first to deny the romantic fiction of the white man.

In the first place there was no hereditary Indian royalty or aristocracy. Even a chief’s son could be set aside in favour of a nephew or even an adopted boy unless by his prowess or wisdom or "medicine" he qualified for the succession to his father’s place in the eyes of the tribal council. The Indians were, of all people, most democratic, and they tolerated castes and "classes" only among certain tribes who were able to lead settled lives. Such were our West Coast tribes.

This is not to say that a chief’s daughter did not have certain advantages. Her father, being a leading man in his band, undoubtedly had greater than average knowledge and skill, which would, perhaps, affect her hereditary legacy. Still, if she did not attain skills in the woman’s role, "brains" alone would not gain her any advantage.

When a man married, he "married" his wife’s family in a very real sense, and, as a member of the family, got the benefits of her family’s protection. Therefore a young man would naturally aspire to marrying a chief’s daughter. Since she would naturally choose only a potentially good provider, great natural ability might become concentrated in certain families. The white men who took native wives would naturally choose those who brought the greatest advantages -- often a chief's daughter.

But remember that in their pre-contact society our Athapaskans had no permanent "chiefs", so if anyone tells you that he is descended from an Indian "princess", don't be too impressed!