This is headcanon
in fact in the Vivre cards, Whitebeard was WSM during his fight with Roger…
note that you don’t know how Whitebeard and Kaido got their titles outside of your headcanon
all we know is that THEY DIDNT BEAT ANYONE for their titles… hence why Luffy didn’t become WSC and teach didn’t become WSM after beating them
in fact in the Vivre cards, Whitebeard was WSM during his fight with Roger…
note that you don’t know how Whitebeard and Kaido got their titles outside of your headcanon
all we know is that THEY DIDNT BEAT ANYONE for their titles… hence why Luffy didn’t become WSC and teach didn’t become WSM after beating them
Even if Whitebeard was considered both the wsm and wsp while being equal to Roger it still makes sense honestly. Roger being equal with whitebeard with his haki hax and whitebeard still being able to fight him on equal grounds
Either way whitebeard proved his superiority over everyone besides Roger. Roger only able to compete with him through hax
Kaidos multiple fights with the emperors and marines are well known. Him being recognized for his strength makes more than enough sense
You keep asking who they beat as if they haven’t proved themselves against the other members of rocks or the marines. It applies to mihawk too they don’t have to beat anyone outright if they prove themselves superior to the rest
Difference is we know Whitebeard and kaido proved themselves through their battles with the likes of Roger, rocks pirates, and marines in the new world
Mihawks most well known accomplishment is fighting shanks 13+ years ago with a bounty lower than a billion