Btw, being a "cog in the machine"(which is just a rhetorical point anyway, this is contrasted later on in the arc. This is a manga for young boys and I trust you guys in understanding it)
does not mean you cant have kings Haki.
Sengoku has it, and he's on record with his famous quote, "are you doubting the government? Just shut up and follow orders"
Meanwhile, Kizaru specifically didn't want to go against his ideals
Btw, do you guys think red puppy isn't a cog in the machine?
Besides personally liking him, there's no actual reason to say Akainu has kings Haki but Kizaru wont have it. Kizaru is literally far less submissive to Akainu then Rayleigh/Gaban/Zolo/Sanji are to Roger/Luffy lmfao
Same with Fujitora obviously
And then you could be like oh well "Greenbull is the exception, he sucks Akainus dick and loves the celestial dragons" and then we simply wait a couple years for you to catch up to the fact that no, GB isn't even really loyal to the government or Akainu necessarily, and has done things behind their backs, and has been shown annoyed with the CD's even
Now to be clear, I don't think any admirals have kings Haki but we don't need to put the users of it on a pedestal. Katakuri has it, and yet he never challenged his mom in like 48 years even when she harmed his family, and was deeply insecure about his position in society. COC users are in fact human beings like anyone else who can get scared/shocked etc, and even wrt Katakuri, Oda made a point that he dislikes making villains who are too *perfect*(of course we could say he does that with his non evil characters, but whatever)so I don't think its a good argument to say Admirals cant have it because they're not generic Madara/Aizen style stoic anime badass villains number 1000