I can see where one can conclude that a certain condition needs to be met for someone born with CoC to actually awaken it. However, I don't think the condition itself has anything to do with personality. The way I see it is:
- A person is either born with CoC or not. There is very little to debate here as the manga has stated it multiple times (up to debate whether it must be inherited from a parent but definitely clear a person is just born with the capacity to use CoC)
- A person born with CoC needs to awaken it for them to actually use it. What is not exactly known are the conditions of awakening it. My theory is the trigger that's needed for awakening CoC is just a major stressor which is why we see people awakening it for first time in life threatening situations (Ace, Luffy, Zoro, Doffy).
At this point if we are going to substitute any life goals/motives as having ambition then all humans qualify. I'm sure there are plenty of people who just want t have a family or that just want peace. To me when we use the word ambition I think of it as a person having some goal that few if any will ever achieve e.g. being PK, being Worlds Strongest Swordsmen, being an Emperor/King of some large territory. In the case of WB, there is no indication he set out to be one of the most powerful pirates, that was just a biproduct of who he is. I'd argue something similar for Shanks but we need to learn more about his motivations.
We also have characters with CoC like BM and Doffy who don't seem to particularly care about anyone but themselves. They have both killed (or were willing to kill) their own family members. They only care to protect their own self interests. So there is definitely a variety of personality types, motivations, etc among known CoC users which makes it a poor indicator for identifying individuals with CoC.
I personally think people are making the common error of missing the hidden variable that is truly what is shared among known CoC users - they are all very strong. Every other trait we mention is not consistent among all the users, except this one. And in the case of strength the causal relationship is CoC -> strength vs strength -> CoC. So even if one believes personality is important it should be CoC -> personality and not personality -> CoC.