Black (Dem.) presidential candidates don't always win the black vote in the primaries, true. But are there any examples where they got a higher %age among white voters than black voters? I can't think of any examples. E.g., Al Sharpton in 2004, when he was getting something like 1% of the vote in the primaries overall, he was still managing to hit double digits among black voters in some states where the black vote was statistically meaningful, according to the exit polls.
So while I don't think it's a given that Booker or Harris will *win* the black vote, if they did better with white Dem. primary voters than black Dem. primary voters, it would be unusual by modern historical standards.
It's worth noting that since 2004, the winner of the black vote (whether that be a plurality or majority) has went on to win the nomination. Even Kerry was doing very well in the early states with black voters (pulling around 40%, with Sharpton getting another 10-20%), and ultimately won closer to 60% of black voters toward the end of the primary contest.
You can actually go back even further and this truth will hold: in 2000, it was a lopsided result in general of course; in 1992 (and by default 1996), both black and Southern white voters were united behind Clinton from the get-go (albeit at a time when the black vote was less influential). Jesse Jackson was probably the last Democratic candidate who won the most black voters in the primary but who didn't clinch the nomination - and even he made an unexpectedly strong showing as a result of it.
