York joining is a complete and random headcanon. BB pirates already have 10 commanders, 9 of them are strawhat opponents, and Kuzan will fight the allies
Nami doesn't have that many fights to begin with to abstract a general rule, same with Robin who's first real 1 vs 1 in the series was against BM.
But we know that there's only one woman commander in BB pirates, and if she fights one of the 2 girls. it means the other will fight a man, which destroys your headcanon of woman not fighting against a man
As I said, almost all of Zoro and Sanji's opponents have a common theme, a serious opponent and a goofy one.