Let's keep something mind: swordsman are the most common type of combatants in the One Piece world. To be recognized as the best of them is a big deal because of how many of them are out there. Not every actor aspires to be the best actor ever, but it doesn't change the fact that the field is stacked with a lot of talent who will beat you out in auditions, or just be chosen automatically due to their name. No one wants to lose a sword duel, even if they don't have the dream to be the best. Zoro has to separate himself from every swordsman in the One Piece world, and beat every single one he comes face to face with. That's not easy.
How Oda spices it up is not through a constant rivalry with someone of similar abilities and goals, but rather Zoro's devotion to someone else, that he's willing to risk his ambitions for.
That said, he does have a back and forth with Tashigi that's a role reversal of the one he had with Kuina in his childhood.