Like he was correct in writing Khan as a white British guy who was driven to commit acts of genocide on inferior beings?
He didn't write Khan as a white British guy. The role was supposed to go to Antonia Banderas, which would have been consistent with the original Mexican-playing-an-Indian motif. You can't blame Kurtzman for a casting change.
And now that I think about it, this brings up an interesting prospect. If for some reason Khan is going to be mentioned in the new Picard series, which Khan will it be?
It will be the one and only Khan Noonian Singh.