its quite simple whether they care about the title or not zoro would see every great swordsman as a potential rival to what he wants to achieve. daz bones flat out refused to be classified as one. I dont think zoro cared whether he was one or not. he simply saw him as something he needs to surpass. luffy isnt going through the yonko because every single one is trying to be pk tho bm has voiced her reasons. he goes through them because he sees them as obstacles regardless of how they feel about the title. the same way he talked down to wb even tho wb could give two shits about the title and was equal to roger at his prime. at the end of the day, the titles arent given because you want it,it usually termed by the world around you after an accomplishment of yours. whether you want the title or not is really not up to you.
or world strongest creature?
