"White privilege" is an imprecise choice of words, sort of like "Defund police," but it stands for a real fact of life. I say it's imprecise because the problem is not that Whites have privileges; it's that Blacks do not have have them. Whites are treated one way because they are seen by other Whites as "people"; Blacks are treated another way, because they are not.
I don't like to call that state of affairs "racism"; I want that word to retain a special bite reserved for those with bad intent. But it's SOMETHING, and "White privilege" has the advantage of prompting White people to think about Black people's situation by attacking their role in it and, therefore, their self-esteem. That makes the imprecision tolerable, I think. Ain't nothing perfect.
Generally, I don't think shaming works. Most people resist it, as many Whites resist the idea of "White privilege." Triggering embarrassment without name-calling isn't easy. But I believe on balance that "White privilege" may come as close to threading that needle as the species permits.