Maybe I'm alone in this thread, but "By Any Other Name" works for me.
It actually comes across as a very Roddenberryan-style TOS story. Kirk and company are overwhelemed by powerful extragalactic aliens, who demonstrate their technological superiority (the ability to instantly paralyze or transmute people) and their ruthlessness (by killing Thompson). The Roddenberryan solution comes in finding the Kelvan vulnerability: their newfound humanity, and exploiting it to bring them to reason. The Kelvans are the ones to learn the lesson of the episode: becoming human on the outside means they become human on the inside.
Is the Kelvan Empire in the Andromeda Galaxy a serious threat to the Federation? Maybe. Kirk may also have recognized that Rojan was simply full of himself and his self-ascribed "mission" to "conquer" and "rule". Once Rojan's crew took control of the Enterprise and set course for Kelva, Kirk had much more than one dead crewman on his mind. Kirk had no idea his ship would survive the Barrier, with or without Scott's suicidal plan. Then when Rojan began transmuting the rest of the crew, Kirk found he had a new mission: he had to restore his crew and stop the Kelvans. Faced with this challenge, and with only a handful of Enterprise crew left in normal form, Kirk wasn't mourning the death of one person.
If I were Kirk at this stage, only three thoughts would be going through my head:
(1: What if these Kelvans actually take my ship to this other Galaxy, turn around, and invade our Galaxy?
(2: How do I stop them and get control of my ship back?
(3: How do I get my crew back to normal form?
I do not see the ending as pure farce, or dismissive of what has happened. Nor do I see Rojan as a mindless cut-throat. Rojan was acting on behalf of his people because his people believe they are in jeopardy. Naturally, when people believe they are in jeopardy, they are willing to kill anyone who gets in the way. Rojan believed the Enterprise crew stood in the way of his ultimate mission: to save his people in another galaxy. Thompson became the first casualty in this galaxy at the hands of Kelvan self-preservation.
Kirk is probably still pissed at Rojan, and for good reason. But Kirk would much rather make peace with the Kelvans, get his ship back, get his crew back, and have Scott figure out how they get the Enterprise to sustain Warp 11 indefinitely. Those are very valuable accomplishments.
As for how Kirk would write the "Dear Mr. & Mrs. Thompson" letter, he would describe her as a heroic casualty of a dangerous "first contact" with powerful alien intergalactic explorers who may prove to be useful allies to the Federation someday. It's obviously outrageous, but given the many times in STAR TREK that aliens have destroyed whole colonies (Cestus III, M-133, Triacus, Delta Rana IV) or space vessels (the Archon, the second Valiant) and yet the Federation starship at hand still pursued a diplomatic solution over revenge, it should not be a surprise. Captain Picard did describe the dangers of "first contact" encounters to Chancellor Durken of Malcor III, and the glacial slog of diplomacy almost cost an injured Commander Riker his life. Picard made it clear that "first contact" is always filled with hazards, even the threat of war.
Given that Kirk managed to avert a larger catastrophe, discovered and made peace with a new neighbor, survived another encounter with the negative energy barrier (a major development), and has seen his ship refit with technology that can sustain Warp 11, he can look upon this mission as a major success... even if the Kelvans tear out all of their goodies and refuse to share them.
Would Kirk try to throw Rojan in the brig? No. But I'll bet he'd persuade Rojan to write an apology letter to Thompson's family. (And I doubt Rojan would object.)