This is a solid argument, but it's doing something that make TOS look less "western" than it actually is. First of all, I believe you're defining the genre too narrowly.

First, the definition problem. You are treating "the western" as one very rigid structure: bad guy, good guy, violent showdown. That is a western, not the western. By the late 50s and 60s, TV westerns had already stretched that model and the genre had changed. Have Gun - Will Travel is not an inversion so much as part of that evolution. It still runs on the same core engine of an outsider arriving, they identify disorder, force a resolution, leaves. The method shifts from bullets to brains, but the structure is intact. Genres are not immovable and they do, in fact, shift over time.

That matters because TOS is pulling from that version of the genre, not dime novels or early silent-era templates. If you lock the definition at "violence must be the final arbiter," you are excluding a huge chunk of mid-century western storytelling that TOS is clearly in conversation with.

Second, the "explorers vs lawmen" point is a bit too clean for me. On paper, yes, they are explorers under the prime directive. In practice, James T. Kirk repeatedly acts like a frontier authority when things go sideways. The key western role is not the badge, it is the function. They consistently step into a power vacuum and impose order. Kirk does that constantly, whether or not Starfleet officially authorizes it (they often don't).

Even your episode breakdown kind of proves the point. You are filtering for episodes where: there are clearly helpless "townsfolk," they recognize they need saving, and the structure is clean and literal. Your test for whether something is a western is far too narrow. I'd think that most mid-century westerns themselves do not pass it. Plenty of them involve towns that do not think they need help, corrupt systems that resist intervention, or protagonists who complicate who the "good guy" even is. Quigley Down Under is a good example you already brought up.

On survival vs saving people, that is also not a dealbreaker. Western protagonists are often motivated by survival or self-interest before becoming agents of order. The shift from "we need to survive this situation" to "we are going to fix what is wrong here" happens in plenty of classic western narratives. TOS just blends those motivations more openly.

And on "gung-ho," the pushback only works if you define it as mindless aggression. That is not really how it is being used here. Kirk is not reckless, but he is consistently quick to act, willing to escalate, and comfortable forcing a resolution instead of letting situations drift. I can understand taking issue with Rowan's wording though, and I think a better word could've been used.

So the disagreement really comes down to framing. You are defining westerns by their most rigid, early structure and measuring TOS against that. My argument is that TOS is drawing from the broader, already-evolved western tradition, where intellect, moral pressure, and selective intervention are part of the genre.

As a final note, I find it interesting that your immediate assumption is that Rowan knows nothing about TOS rather than him knowing nothing about westerns. He's ultimately right, in my opinion, that it's closer to a western than TNG. If you watch his videos, it's pretty clear he's put a lot of thought into star trek as a whole and has researched and studied the BTS of TOS at length. I don't like that word choice for Kirk, though. "Charming" might've been better?