Does it? I think that's a different question.

Consider European genocide of Native Americans. Suppose they all had been wiped out. Or consider German genocide of Jews, with the same hypothetical. I think the "sins of thy father" question is: Should the descendants of the criminals be punished for the crimes of their ancestors?

My answer to this is "no". And I think bringing it up in this context mainly confuses things.

I think the question of privilege is about present-day social inequities. If the question is, "Should we work to make society fair to everybody, no matter their race, gender, sexual orientation, or other irrelevant factor?" There, my answer is a firm "yes".

Will that involve people with unearned privilege giving up that privilege? Sure. But that's not a punishment for being among one of the privileged groups, no matter how much it feels like it.