Yes, I agree with you.
Our suggestion to some of our white friends--inclusive of the POCs whose highest goals is to embrace whiteness even when they aren't 'officially' white--is in part addressed by Dr. Brian Lowery's work in Organizational Psychology.
Dr. Lowery states that at least some of our forward motion is due to white people ACTING on admission of their privilege, just as they point out. One of his studies notes that white people as individuals are eager to admit that other white people have privilege, but when it comes to the particulars of their own privilege, they revert to the concept of 'merit.'
This is based on the human proclivity to self-serving attribution: studies show that humans tend to credit themselves (intrinsic) with their successes but credit outside malign forces (extrinsic) for their failures. Similarly, most people tend to see others' successes as extrinsically gained and their losses due to their failures. Thus, people tend to give themselves more benefit of the doubt than they give others.
If this individual behavior is extrapolated to a collective/community level, we can observe that, only in the case of privileged people is this perception distorted. In other words, in the case of white privilege, there is a much higher likelihood that the individual will have gained due to EXTRINSIC PRIVILEGE yet will attribute that to intrinsic achievement. Frankly, this is the behavior that POCs like me witness (in my case, for 30 professional years and more than 50 lived years) and find bizarre.
Lowery implies that each white individual negotiate this reality HONESTLY: that is, each time a white person is privileged with something, they immediately default to 'I got it because I'm white,' NOT 'I must have earned it due to my merit.'
Because this goes against the normal tendencies of humans, it will require EXTRA work by white pp, and it will feel strange. For example, my WOC friends and I discuss the way that, over a period of decades, no matter which POC earns the promotion, a white person almost always seems to get it. Why is it that they perceive it as 'earned' when we almost always see it as 'for free'?
It is because we are ONLY a white supremacist world. Thus, only white people need to ask these questions. If you are in a position to dole out these rewards--which include prizes like the Academy Award, publications of books that virtually always go to white women, or promotions at any corporation--keep in mind that white people tend to believe that only white people are capable of leadership: admit that internal sense of superiority. Then, ACT as if that internalized superiority is a distortion of reality: that what seems 'earned' is actually 'gifted.' The next step would be for that white person to admit that, each time these gifts are accepted, they are almost always accepted at the expense of a POC, especially in competitive arena which are desirable. Then, ACT. Is it right that POCs hit a chlorine ceiling over which even nonperforming white pp seem able to climb?
You are right: it must be performative. White people as individuals must go further: they must overcome the human desire to perceive oneself, inappropriately, as intrinsically worthy of reward when the reality is extrinsic. This won't feel good, as Dr. Lowery points out, because all people want to give themselves credit for success.
But as you point out, not all people need to do this: white people do. They should be. Do not assume the white privilege is 'over there.' When you get something, default to 'privilege' not 'achievement.'
This will not immediately change the construction of these white neighborhoods. White neighborhoods are white because white pp have money, and they have money because they give each other promotions and prizes. This proclivity should be resisted consciously in order to move forward, and if it is at that personal, individual level, I think we will see those neighborhoods becoming more diverse.
Take a look, if you've gotten this far: