Well if (as you said) determination and effort are what it takes to overcome disadvantage, then there is no white privilege.
Saying some can overcome an advantage isn't saying most can or that everyone with that advantage will fail to utilize it or work as hard.
And that's before you consider the question of how many places there are at the
plenty table.
White people don't have a monopoly on effort.
I agree, but they don't have to. They only have to have the advantage and the ratio.
Look at it this way. You have one hundred people in a room. 12 of them are black and 63 of them are whites with that privilege. For the sake of argument lets say twenty percent of both groups are slackers. Now we have (rounding) 10 blacks and 50 whites vying for the same seats at that table. Now let's say ten percent of those are exceptional in talent, will be hard to keep out of the winners circle. That means 1 black and 5 whites are grabbing the brass ring out of hand, leaving 9 blacks and 45 whites in the lesser group whose efforts will be highly competitive. So whites begin with a pretty hefty likelihood of finding the limited remaining seats of power. And there will be a gradation of degree of ability to make that seat which will inherently work against the outlier and for the entrenched via that ratio.
So you can see where the odds rest, provided the playing field is fair, meaning there's no element among the power structure tilting the field. Unfortunately, we also know that's not the case, that systematic discrimination has been the history of our nation and that we've had to enact laws and even alter our Constitution to combat it.
When that still existing problem is reflected even subtly within the hiring and empowerment structure it takes those hard odds and few seats and makes advancement, beyond the few who are hard to deny, a long shot. Which means you'll see it, but it won't approach the rule.