It does break it if one wishes to reconcile Voyager with "Where No Man Has Gone Before" or STV without pretending they didn't actually travel to the rim or centre of the galaxy as shown.
The point is that it doesn't "break" because it
bends. It's imaginary, not real, so everything is subject to interpretation. Details can be glossed over or rationalized, and the overall conceit of a coherent reality survives. After all, the whole thing is just pretend, so it's easy enough to pretend that something wasn't precisely what it was claimed to be in the past.
I'd say a lot more than a few ultrafast journeys "slipped through" - off the top of my head...
TOS: Where No Man Has Gone Before
TOS: By Any Other Name
TAS: The Magicks of Megas Tu
Star Trek V: The Final Frontier
TNG: Conspiracy
Star Trek: First Contact
ENT: "Broken Bow"
Star Trek: Nemesis
Star Trek
Star Trek Into Darkness
Out of more than 720 episodes and films. So that's only about 1.4% of the whole. Not too bad an error rate. (Although you're forgetting "Is There In Truth No Beauty?", which also involved crossing the galactic barrier.)
But yes, there are elements of some of those that need to be disregarded. I'm not saying otherwise. Canons disregard their own past mistakes all the time. My point is that it doesn't "break" them to do so, because they're intrinsically flexible. Indeed, you've got it backward. All canons have inconsistencies, so the illusion of reality depends on the willingness to gloss over, rationalize, or ignore the parts that don't fit. What "breaks" that illusion is the refusal to do so.
In the case of "Magicks," the entire conceptual underpinning of that episode, the steady-state theory of cosmology, has been thoroughly debunked by the overwhelming evidence in support of Big Bang cosmology; thus I consider the whole episode to be as apocryphal as "Threshold" or "The Alternative Factor." There's really no way around that, since the steady-state nonsense is so inseparable from the story. And of course many subsequent Trek episodes have referenced the Big Bang, so we know it's true in-universe. A canon is entitled to overwrite its past mistakes, including scientific mistakes.
In the case of ST V, conversely, there are only three near-consecutive lines in the film that mention "the center of the galaxy" at all. If one chunk of dialogue maybe 20 seconds long were cut from the film, the problem wouldn't exist at all. So I'm content just to ignore the reference, since it has no real relevance to the story.
All your other mentions are simply of instances where ships got from one place to another unusually quickly. That's largely just poetic license, driven by the needs of the story. But it doesn't "break" anything, because the creative mind can bend. For decades, since at least the 1980
Star Trek Maps, fans have been theorizing that warp velocities vary depending on the conditions of different parts of spacetime. That idea has even been stated outright in the
TNG Technical Manual and
ST Encyclopedia.
As for the new movies, the 2009 film was cleverly edited to suggest a very quick jaunt from Earth to Vulcan while actually incorporating clues (such as McCoy's costume change) that considerably more time had passed. So that never bothered me. Granted, STID does show the
Enterprise getting from the Klingon border to Earth in mere seconds with continuous dialogue and action throughout, so it's much harder to justify there. But mistakes happen. They don't "break" the canon because canons have the built-in ability to absorb and repair damage.
My point was merely to illustrate that there are bigger and more fundamental continuity issues in Trek than those presented in Enterprise.
I don't agree that starship travel times, or indeed any technical considerations, are "fundamental" issues. What's fundamental to a work of fiction are the characters, relationships, interactions, ideas, and emotions. The technical matters exist only in support of those fundamentals. Unless it's a work of hard science fiction where the scientific premise is the core driving idea of the tale, but then,
Star Trek has never purported to be that. It's aspired to be more scientifically credible on the whole than most SFTV and film have bothered to be, and occasionally has done a good job living up to that aspiration (although only occasionally), but it's always been primarily about characters, ideas, and adventures.
^^Problem being they left the galaxy at the rim, not by travelling "up" or "down"
From "By Any Other Name"...
ROJAN: There is an energy barrier at the rim of your galaxy.
KIRK: Yes, I know. We've been there.
http://www.chakoteya.net/startrek/50.htm
Thus placing both it and "Where No Man..." at the galactic rim, far far further out than you (and the 2002 Star Trek Star Charts) postulate.
That's defining "rim" far too rigidly.
The dictionary says it's "the outer edge, border, margin, or brink of something, especially of a circular object." Yes, "especially" of a circular object, but not invariably. It can just as well apply to any border or margin. For instance, the same dictionary says that in metallurgy, the rim of an ingot is "an outer layer of metal having a composition different from that of the center." In other words, the entire outermost surface of a 3-dimensional object. So there's no reason the word "rim" can't be used in that sense. And even if there were, it would still be simple enough to ignore
one single 3-letter word in the name of common sense.
And really, it's simple logic. The idea stated in "By Any Other Name" is that the barrier precludes safe entry or exit into the galaxy. Therefore, it must surround the whole galaxy, not just be a narrow strip around its outer edge like a bicycle tire, since in that case it would be easy to go around it.
