Not really because very rarely in this manga is the torch passed down to someone genetically related to the torchbearer.
The warlords are more notable than Yamato or Katakuri anyways.
Genetic relation
is a big deal in the One Piece. Thats why executing Ace was the event that wrapped up the first half of the manga. That’s why Weevil was using WB’s name for the clout.
Now we have a scenario where the same line up of monsters on the Rocks Pirates now all have their offspring under another pirate challenging the world. WB, Big Mom & Kaido were the highlighted members of the Rock Pirates…now we have the sons & daughter of those 3 following under a single pirate again? Of course the world would see that as the second coming.
The Warlords simply don’t have the same relationship. It’s not the individual like Katakuri or Yamato that matters, it is the name on the Rocks Pirates that does. The terrifying part in hearing the “daughter of Kaido” is the “Kaido” part.