Cause they are no superficially thinking children who care about their individual fame and D length comparisons.
Admirals are either lazy monster (Kizaru, prob Greenbull), or they are determined in justice (Akainu, Aokiji, Fuitora). No childish and lofty desires here.
Akainu never cared about going around and challanging others in order to be considered the strongest by fodders. He knows that he would crsuh anybody if it comes down to it. He's not "all talk" like Crydo, he proves his power in fights. That's why he had not a single doubt about his strength when facing the World's Strongest Man and Pirate and basically killing him at Marineford.
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@Fleet Admiral Lee Hung still living rent free in your head, I see...