The fact that Admirals are subordinates I wasn't trying to argue for their lack of CoC I just wanted to compare Coby and Zoro's dreams in the context of how reasonable it would be to compare them when we're talking about Mihawk's CoC.
No just because Coby dreams of becoming an Admiral does not make it a Kingly Ambition. Same goes for WB's desire to have and protect a family. I don't see the point of it and it was never mentioned in the Manga.
1. Yes but I didn't say that for CoC you have to necessarily fulfil your dream I just pointed it out to clarify the difference between them and Mihawk.
2. No.
3. just because King wants to fulfil Kaido's expectations doesn't give him Kingly Ambition and has nothing to do with Mihawk.
The King and Zoro are similar in that they both
want to help fulfil the dreams of their Captains, except Zoro also has his own dream of becoming WSS which has been confirmed to be Kingly, which is funny.

4. Ok
I didn't say that only WSS and PK are Kingly Ambitions.
I said that only PK and WSS were mentioned as Kingly Ambitions in the context of CoC.
I.e., I see this as a direct implication from the author that to become a PK or WSS you need to possess CoC. That's why I point to Zoro and say that the biggest and most important enhancement he got after timeskip was CoC.
Zoro and Mihawk are not the same character but can we stop pretending they are not related lol.
If you don't like the wording 100% then I can say 99% but I don't see the point of allowing the possibility of no CoC for Mihawk given what we have now.
Once again to clarify, I don't think you need a certain Ambition or any Ambition at all to have CoC.
Mihawk having a CoC is common sense given his WSS title and the way Zoro is approaching becoming one.