I have trouble figuring out who Kirk is sometimes. I'm not writing a story, but if I were I'd have to think hard about what Kirk is all about.
Speaking personally, Captain James T. Kirk as portrayed by William Shatner is very well defined. Given the totality and span of material (I am old-school 'canon' just legal right-holders produced live-action (though I won't argue inclusion of TAS)). We know who he is just as much as Mr. Spock and more than the other characters of TAS. Based on what we know of him we could reasonably predict his overall behavior and reactions. We know roughly what to get him on his birthday and what topics not to bring up in conversation ... what more do you want or expect?
I also respectfully disagree with the pov that Shatner had to put more work into his character than Leonard Nimoy did with Mr. Spock because I don't believe that is true. According to many sources, Nimoy was very concerned about things making sense, being reasonable and well motivated. He worked things out and strove to fill in gaps. Leonard practiced due-diligence and did his homework in preparing. It is also why his input into the TOS films (especially III to VI) was so invaluable.
But again I gush.