What we get is what we get, though. So fan rationalizations are the ultimate word on the issue!
We just need to consider not just what we have so far, but also what we might get in the future, so our rationalizations won't backfire. Are individual patches and symbols going to make a comeback? Probably not in any "future" production, because Star Trek has abandoned the practice long ago and isn't comfortable with it. But with "past", "prequel" productions, the creators are likely to be well versed in Trek lore, and it's fashionable to milk the lore (regardless of franchise, but especially in scifi) for fancy details, of which these patches might be one.
Truly ship-specific patches in ENT would be a United Earth Starfleet thing, a bridge between now and Trek, and not a "problem" or an "issue". What we have in TOS is an anomaly we need to explain away, though, since the arrowhead rules supreme in UFP Starfleet in general, and also in modern flashbacks to days during and before TOS. "Ship-specific" doesn't really cut it to begin with, since some of the TOS badges spanned more than just a single ship already.
But we might go for "Fleet-specific", now that Trek post DS9 acknowledges the idea that Starfleet would feature many distinct Fleets; perhaps our cameras have always been pointed at the First Fleet, except for a couple of times in TOS*? The other way to go is to plead different branches of the service, but that sounds a bit hollow when two of our unique patches come from sister ships to the hero ship.
In the end, our "ultimate word" is fairly unlikely to get challenged. But at least one of the spinoffs under works, Strange New Worlds, is going to try and exploit the TOS niche of storytelling. When we spot our first sister ship in that show, then we can tell...
Timo Saloniemi
* Kirk did seem awfully ill versed in what the sister ships were doing. Perhaps each Fleet would have one of those, and the Fleets don't share itineraries much?