Admiral Cartwright as played by Brock Peters is one of my favorite. Peters was a powerful actor and I enjoyed watching just about anything he was in.
Reading thought this thread however, it occurred to me that there was a missed opportunity with this character. Cartwright never we established to have "history" with Kirk that is noteworthy. He was there in TVH and that's about it. To Kirk, he was just another admiral.
Cartwright was, as mentioned upthread, sort of a soft-recasting of Admiral Morrow. Early scripts for TVH had Morrow, not Cartwright. I don't know what circumstances led to this change, but had they continued with Robert Hooks as Admiral Morrow, we could have had a scene in TVH with him and Kirk. Why would this matter? Go back to TSFS - Morrow was the first onscreen Starfleet admiral shown in any of the films (aside from Kirk). And he was Commander of Starfleet to boot! In the movie, Kirk and crew defy orders and steal the enterprise to rescue Spock. In a real sense, Starfleet served as an antagonist to Kirk. But Starfleet is an organization - a "thing", not a character. Admiral Morrow however, is a character. In the story, he serves as the embodiment of Starfleet. When Kirk disobeys orders and defies Starfleet, he is betraying Morrow's trust.
We never get closure on this act - in TVH Morrow has been replaced by someone entirely different. On top of that, Kirk's "trial" and consequences don't even come from Cartwright - they came from the Federation President. Cartwright and Kirk never even talk to each other.
If Morrow was in TVH instead of Cartwright, I keep thinking that the ending would resonate much more if Kirk could be confronted with the person he disobeyed. They can still keep everything else the same with the Federation President and council chambers - and just have him add a line to say "at recommendation of Starfleet's Commander, all charges but one are summarily dismissed" with a quick cut to Morrow. After the trial, Morrow finds Kirk in the crowd, and says something like "Jim.. you've become a hell of a pain in my ass. But that was some pretty quick thinking by you and your crew. Nice job"
Flash forward to TUC - now imagine how much of a kick to the gut it would be to learn that Morrow was heading the conspiracy. With that history - with the man that Kirk disobeyed, and who salvaged his career to be the conspirator, setting him up to be the fall guy - now that packs a bigger punch. I mean, I would hate for him to go bad, but Meyer wanted to go that direction anyway - might as well go all in.
The flipside of this is we would have missed out on Brock Peters. Maybe you can have both of them in TUC. After all, they invented a new level "C in C" with yet another admiral we never saw before. Have that one be Morrow.
I think a lot of this falls on the production of TSFS - depicting everyone else in starfleet as arrogant or ineffective just to make our lead characters look better. But they weren't made with story arcs planned out - they were essentially making it up as they went along. I think since TVH didn't have Morrow for whatever reason, they worked with what they had.