I'm going to write an article about this at some point. But to answer you question with a question for now, why do you think that teaching white children that they're privileged helps undo systemic racism? What's the causal mechanism that leads from one to another?

If ordinary white Americans recognised that white privilege existed, what do you think they would (or could) do to help black people?

White privilege is almost always taught in a punitive way. "You have this advantage and the poor black people don't." What are white poeple supposed to do with this information? It's not only simplistic, it's wildly incomplete. For example, did you know that only 15 percent of Americans are over six feet tall, yet 60 percent of CEO’s are over six feet tall? Being tall confers a huge number of other advantages. Especially for men. What do tall pepole need to do about their privilege? Should we teach tall children about it in schools? There are a huge number of other "privileges" like this that have nothing to do with race.

Change happens when we help the disadvantaged. Not when we chastise the advantaged. And certainly not when we pretend that a single type of advantage is the defining measure for human existence. I'm for helping black people who have been disadvantaged for the colour of their skin. I'm for punishing people who are actually involved in keeping black people down. But stigmatising all white children because of the colour of their skin is not only self-evidently wrong, it doesn't achieve anything. Except, maybe, make them resent black people.