I don't buy the argument that it "limits the drama" to know a given character won't die. Everyone who watched an episode of TOS back in the '60s knew that the heroes wouldn't die at the end, or that if they appeared to die, it would be reversed somehow. That's pretty much a given in any ongoing series, most of the time. You know the heroes will survive, but you choose to buy into the conceit of danger for the duration of the story. The interest is in seeing how they survive and triumph, not just whether. It's like watching sports. If the only thing that mattered were knowing whether your team won or lost, there'd be no reason to waste hours watching the game -- you could just read the results in the paper afterward. You watch because it's not just about whether they win, it's about experiencing the struggle along with them.
Besides, it's not as if a character's death or avoidance thereof is the only possible thing to tell a story about. There are many other sources of drama. For instance, in "Court-martial," what was more dramatic and engaging to the viewer -- the question of whether Ben Finney would kill Kirk in their obligatory tacked-on fistfight, or the question of whether Kirk's career and reputation would be ruined? If it were only the latter, why even bother with the preceding forty minutes of story? What makes drama isn't just physical danger, but emotional danger. Drama comes from a character having something to lose, something that's meaningful to them. There are lots of things other than just staying alive that are meaningful to people, lots of things they can be hurt by losing -- their relationships, their reputations, their ideals, their confidence, you name it. Even if death is involved, it can be the death of somebody else, someone they loved or were responsible for, that's most devastating to a character.
I also question whether Nogura and Terrell really count as "connections back to Kirk." Sure, Nogura was Kirk's boss for nearly three years, but he was the boss of everybody in Starfleet. And let's not forget that Nogura never even appeared onscreen in TOS; he was just mentioned in passing in one movie. So it's a stretch even to consider him a TOS character. As for Terrell, he explicitly stated in TWOK that "I've never even met Admiral Kirk." Their only direct interaction was on Regula I and the planetoid, and Terrell wasn't even himself then.