First, that's a ridiculous analogy. Second, your "evidence" doesn't even provide a consistent scale size. The ship grows and shrinks depending on how they decide to match interior to exterior. How is that reliable? It was an image superposition where one image (ship) was arbitrarily scaled up so the second image (people / shuttles) would fit in and the composite would "look cool."
Anyway, Kirk's personal escape pod is seen being ejected from one of these hatches. No way that thing was 5m in diameter. Does that "evidence" get thrown out?
Look closer. The hatch is only half the size of it's outer collar... and you might want to have a look in those windows too - they're about the size of the bridge one. See inside?
I really don't care what artists think the size is, based on their need to make something "look cool."
Well in that case you're screwed, since the Enterprise was designed to look cool - in 1964. Every single ship in Star Trek's 46 year history has been designed with visuals first and foremost in mind.
That's why there's a term "artistic license", which means to stretch the truth because you can.
I match the form with the function. The Enterprise shouldn't have 5m diameter hatches. Who thought of that? Can you explain what they're for? It makes no sense for the ship to be over 200m tall (as high as a 70 storey building). etc... etc... etc... Shall I repeat: THOSE DIMENSIONS MAKE NO SENSE.
Form with function as it relates to Star Trek? Shouldn't you be trying to convince me the Enterprise is the shape of a rocket, or perhaps spherical? What sense does the Enterprise's shape make in the first place? What sense was putting the bridge on the very top level, completely vulnerable?
And how do you define "making sense" with regard to a fictitious spaceship? It's all make-believe
. The old Enterprise can be 289m while this one can be several times bigger with no trouble at all. Remember that insanely huge mushroom-shaped spacedock in the classic movies? If Starfleet can build them, ships like the USS Enterprise and the USS Vengeance are nothing in comparison. There is NO in-universe reason why they can't be the sizes ILM claim, and no real-life reason, either.
I'll say again, you're arguing what you want the ship to be and not what it actually is in the film.