I said that the admirals we have now (Green Bull, Fuschia Tiger, and Yellow Monkey) don't have it. Akainu also doesn't have it. Kuzan is essentially guaranteed not to have it. So saying that they have kingly ambition is not true. If they are revealed then that means that they do, simple as that, but it has not been revealed as of now.
I never said that being an admiral in general, past or present, is mutually exclusive to CoC. That is your error in reading.