I think they have as much as any individual in a superior position.
So, none.
You seem to believe that white men in particular have some need to hold onto their superior positions.
Anyone in a position of superiority that benefits from a system designed for their success is going to want to hold on to that power. You are correct in that there is no widespread White supremecist mentality in America today. But we still are living in the America that started with the 1790 Naturalization Act and White people have really shown us in the era of Trump how desperate they are to hold on to their "rightful" place in America.