Why shouldn't it be a thesis on interplanetary relations, if there is enough information given in the episode to support it?
As for Trek's solutions not being solution to real world problems, I think it's fair to say that Trek's solutions can inspire solutions to real world problems.
Why? What would Rand have added that Tamura didn't? Tamura was presumed to be a competent member of the crew, and I certainly didn't see her whimpering about being "frightened" (my only complaint about TOS-Uhura). The "look at my legs" line Rand had in "Miri" was equally cringeworthy.
But how do we know that's what the people of Vendikar were doing? Yes, the computer would have registered the requisite number of deaths, but how do we know that's what was really happening? Someone on Vendikar could have reprogrammed their computers to make it look like people were dying when they weren't.
Or for that matter, there could be no one left alive at all on Vendikar - just a computer, carrying out its programming.
Barrows and Landon seemed to bring something to the table but the other Yeomen were just ciphers in skirts. While I agree that Rand as a character was often not well written, using a recurring character allows more personality to shine through. Noel was originally Rand too. While I love Noel, I have to admit that it would also have been a great part for Rand, giving her agency and action that her previous roles lacked. It could have helped revolutionise the character.
Uhura also gets scared in Mirror Mirror and Plato's Stepchildren!
I agree with your other points though. I would have preferred it if Kirk had possessed some additional information on which to base his hypothesis. I do accept though that the allegorical nature of the story meant that the root of the conflict was left deliberately blank (not even vague) but he looks like a chancer.
I really am not comfortable with this whole conversation. If it were merely about Kirk and his decision making is one thing, but to bring politics into this. I think it's far better not to bring that into discussions about ST. They always say not to talk about religion and politics in mixed company. It staves off potential blow ups
The politics is just a backdrop to provide the context for allegories. Is there any point in discussing Let That be Your Last Battlefield without understanding it's real world context? I'm genuinely fearful of where some real world decisions might lead but some politicians still take that leap. Kirk does the same.
I wonder more generally if idolising that kind of hero by making them succeed through luck rather than research, hard work and compromise means that domestic politics becomes more blinkered. Kirk does make mistakes too I suppose.
It might be interesting to consider what real world point they were trying to make? Are they advocating abolition of the nuclear deterrent? That seems to be the closest parallel.
It does raise an interesting question as to what the root cause of the conflict might be. It doesn't seem to be about land. Is it pure racism, religious and philosophical, or human rights abuses?
Also, if each planet ends up with an extra 3million people each year, what does that mean for their infrastructure going forward. Soon, they may need land, and we're back to square one :-P. One of the more interesting TNG allegories was the one proposing that retired people should be retired permanently at 60 to control population. That's a real world problem that's steadily getting worse!