First off, you're doubling down on the same mistake that I just pointed out: Equating "military" with "warlike." Calling something military is not about whether its purpose is war, peace, or exploration. It's about whether it's a government-sanctioned armed service with a rank structure. There are military bodies whose primary purpose is peaceful, like the US Coast Guard or the Army Corps of Engineers, and there are military bodies whose purpose is scientific, exploratory, diplomatic, etc. (Starfleet is largely based on the British Navy in the age of exploration. Its ships did a lot to advance the cause of science and discovery.) After all, it's not like the military ceases to exist when there isn't a war on. Militaries have a wide range of different responsibilities, many of which are peaceful. So your quotes about Starfleet's mission being peaceful or scientific are not relevant to this issue.
With all due respect, my intent was to double down on the fact that within the shows themselves, Starfleet has been said to be not a military (pretty black-and-white). In retrospect, some of the quotes I picked were kind of weak (like the
Voyage Home one), so I get your point.
Also, if you want to play the quote game, there are canonical quotes that explicitly do define Starfleet as military. In "Errand of Mercy," Kirk tells the Organians what Starfleet can offer them, including "military aid."
There was a war, and no one's denying that Starfleet will pitch in when that happens. The question is, do they do that as a military, or as another organization? (That might seem like a stupid question, but we have canonical evidence that it's not a military, so I think it's worth asking. It's also a more interesting conversation than just dismissing one side as a script error or the result of something the creators didn't think out, or whatever.)
In "Obsession," he asks Garrovick for his "military appraisal of the techniques used against the creature."
A simple way to label tactical analysis?
Garth of Izar refers to Kirk as "one of the finest military commanders in the galaxy," and though Kirk says he prefers to think of himself as a man of peace, he doesn't refute Garth's characterization.
Garth is also totally wacko at this point, so everything he says needs to be taken with a grain of salt. Case in point, his explosive. Did he event a powerful explosive? Yeah. Was it the most destructive force in the Galaxy, like he said? Probably not. Could Kirk be good leader in battle? Yeah (see "Balance of Terror" [TOS])? Does that automatically make him a soldier? No, since Kirk could have had tactical training with or without being in the military.
In "The Way to Eden," Kirk says the Romulans will see the Enterprise's presence in the Neutral Zone as "a military incursion."
What the Romulans would see it as may not ascribe to objective reality.
David Marcus twice refers to Starfleet as "the military" in TWOK.
Maybe. I have wondered about this one on occasion. However, Marcus is not really an expert on Starfleet, so, comparing his statement with Picard's from TNG, the latter would be more accurate, since Picard would know exactly what line of work he is in. It's hearsay, like you think Worf and phasers are, IMHO (and I think that Worf is a more credible source on phaser history than Marcus is on Starfleet). Also, at least one of the times (when claiming that scientists have always been the pawns of the military), Marcus is pretty agitated.
In "The Icarus Factor," Picard cited Riker's "military proficiency."
See the comment for the "Obsession" example.
In "The Most Toys," Fajo called Data "a military pacifist" and wondered why he was in Starfleet if he didn't believe in taking life.
Like Marcus, Fajo is not necessarily an accurate source of info on Starfleet and is actively trying to manipulate Data.
In "Paradise Lost," Sisko refered to Admiral Leyton's plan to impose Starfleet control over Earth as "military rule" and "a military dictatorship."
That's what Leyton wanted to create. I'm not sure that's conclusive proof, since one could argue that Sisko was using a technically incorrect term to convey the practical end result, however, I never saw this episode, so I don't have enough details to really comment on this.
And while we're at it, there are a number of instances of characters using the word "civilian" to refer to non-Starfleet personnel. In "The Perfect Mate," Picard said "I have confidence in the self-control of my crew, Kamala, but there are guests and civilians on board." In "Lower Decks," Ben said "I'm not Starfleet, I'm a civilian." In "All Good Things," O'Brien referred to "Freighters, transports, all civilians. None of them Starfleet ships."
I honestly took it that non-Starfleet people would be called civilians, to distinguish them from those in service (like how workers in a factory could call non-employees "civilians, "despite not being military). So, I don't think this one really supports either side.
So the instances of Starfleet being explicitly called military and non-civilian outnumber those few instances where writers mistakenly make characters say that it isn't military.
Starfleet has
never been called a military anywhere in the canon in word, so we have far more instances where it's not called one. And "writers mistakenly make characters say that it isn't military"? That's the exact same argument I was using for the arrowhead patches. I'm confused, what's the difference here that it's a valid model of explanation (esp. given that we have concrete evidence, instead of needing to guess based on some odd props that were never explained)?
And of course, we've seen that Starfleet does defend the Federation in wartime, plus it has ranks, uniforms, and courts-martial. It overtly and routinely functions as a military. There's nothing else it could be.
Ranks and uniforms could be used completely divorced from their military origins (like the Salvation Army and the Boy Scouts prove). The court-martial I can kind of see, unless Starfleet borrowed the term for their own review and discipline hearings. Question: could a civilian represent the defendant in a real military court-martial, like in "Court Martial" (TOS)? (In all honestly, I think Starfleet is a sort of paramilitary organization that has no true analog to any modern organization, given that they undertake some military operations despite explicitly not a military. I think that divides the difference, as you put it with the patch question.)
As far as Starfleet defending the Federation, yeah, one of its services is to defend the Federation, however, that is not what it was chartered for, is not it's main objective. Even if a military works on scientific and humanitarian projects during times of peace, it's first duty is still to defend it's nation. For Starfleet that's a secondary objective, at best?
Also, if it were a military craft, how would that work with it's exploration? Would be an act of war if it went into another nation's borders by accident? I mean, what would the legal ramifications be of sending warships to explore the unknown?
Have any of the people who worked on the show addressed the military question, by any chance?
Good grief, you're not even trying to think about this. You're just ignoring everything I say and repeating your same unquestioned assumptions. I'm talking about the laws of physics. That overrides everything else. Think of wheels. Think of boats. Think of all the things that are always the same shape because they physically have to be, because there is simply no other design for them that can perform that function. Every alien civilization in the universe would be bound by those same laws of physics, and thus their designs would have to conform to certain unavoidable basics.
Darn it man, I'm a graphic designer, not an engineer!
In all seriousness, it would help if I knew which components "needed" to look alike and which could vary, given that I have no frame of reference any of that. You're insisting that they must look the same, but have no idea what parts to even analyze here.