The exertion of actions which create the state described as White Privilege are entirely, literally to do with racism. The answer you gave to solving racism is therefore apt in this case. Some people will counter by saying "I'm not a racist!" and it has to be fully accepted that they're not - but that doesn't mean that the unconscious actions of people don't sometimes lead to situations of privilege being unintentionally created.
That's my point though. Racism is the problem, not white privilege. As I've said before, the desired end goal is that everyone has the "privileges" that are currently extended to whites. You don't actually want to get rid of white privilege, you just want other people to be treated just as well. I guess it's technically not a privilege if everyone has it, but I doubt the general populace thinks of it that way.
The issue with calling white privilege the problem is that suddenly anyone who has the good fortune to be born white is part of the problem. I'm no more a fan of that than I am of labelling all men as part of the problems of rape and misogyny.
There are several posters in this thread who still labour under the misapprehension that White Privilege is a set of actions being undertaken entirely by white people - but it isn't. The study that I linked some pages ago is a good illustrator of that. The state of privilege (class privilege too) comes from the preconceptions of other actors in those scenes - addressing that social programming is the key to creating a state where no person is conferring any kind of privilege consciously or unconsciously based on their perception of another person's colour or class.
Which is neither here nor there. It's still at it's heart just societal and cultural scale racism. But how we label things matters. When you label something as a problem, the natural human response is "how do we get rid of that?"
If that problem is described as culturally engrained racism, that's great. You're looking to remove the cultural issues.
If that problem is described that white people have it better than others, that's scary. You're either looking to remove the privilege or the white people.
White Privilege is a terrible phrase that has a very specific and non-intuitive meaning within academia, and is a somewhat debatable choice even there. In public speech where people will take it at face value it would be remarkably close to hate speech if there wasn't this perception that it's somehow impossible to be racist against white people.
While there's an argument to be made that people should learn what it means and stick to that, I think at some point when you're using terms that can easily be misconstrued within the context of the discussion it just becomes a bad name. Calling it Culjerul Fliggerbonnom would be less confusing, because that has no prior meaning or baggage attached. People would just ask and get an explanation of the term. If you say white privilege, people think they know what those words mean, and it's not at all obvious that the real meaning isn't even close.
And once enough people start using the common sense intuitive "definition" of white privilege, ie. whites have it better than everyone else simply by virtue of being white, it becomes a thing. And that's not correct.