I think most Admiral fans hate CoC from the bottom of their hearts, the reason they mess with the Admirals comes from the love of their devil fruits in the first place. The only thing is a lot of Admiral fans simply believe they will end up with it because the story is basically headed in that direction where you aren't a top tier without it.
So it's not that the Admiral fans want CoC, Admirals are already fully established top tiers with or without CoC unlike the other two characters here, it's just that most think realistically they will end up with it. We already know Sengoku had it, only a matter of time till Akainu is revealed to have it, which would basically mean so does Kuzan and so on so forth.
As for Law, Law fought beside someone who was a confirmed conqueror, and Oda completely shafted the conqueror in favour of Law. So Law fans didn't even blink or think twice about CoC, not only because of how they know he is in good hands, but also because his ability is like advanced CoC on steroids, he literally has little use for it unlike someone like Luffy who desperately needed something to take his damage capacity to the next lvl. So I wouldn't say Law fans ever gave two shits about CoC. Again only recently is the manga headed in the direction where CoC seems to be more common than we originally thought, hence it's only natural people would suspect Law being such a central figure of this era will end up with it. Not for powerscaling purposes but just from a pure narrative standpoint, adCoC is absolutely unnecessary for Law, but it's just hard to imagine him without it at this point given his importance to this generation. After all he will be a legend in his own right.
So with everything stated above, naturally Sanji is the clear choice. He desperately needed something to put him over the top. Without a devil fruit or top tier haki, germa genes can only take you so far (I mean just look at Germa, who is the strongest of that bunch? Dude barely above Vet lvl if that?). So it made sense why Sanji fans would be most desperate for it.