It's because people can't ignore the throwaway lines that it gets tiresome.
No such thing as what "people" can do. Some people yes, other people no. I daresay the majority of viewers don't obsess over the nitpicky details the way a few tend to do. It's just that those few make a lot more noise about it.
Things that affect the plot are certainly part of world-building and worth remembering. That's why I'll grudgingly accept that the Romulans having cloaking devices in the Enterprise era is questionable. Although I also find many of the conceits in Balance of Terror to be clumsy ways for the episode to more closely emulate Das Boot.
There have been countless cloaking-device inconsistencies over the franchise. "Enterprise Incident" cloaks were completely undetectable, but ST III cloaks had a visual distortion. That distortion was gone by ST VI, and the cloaks could be detected by their ships' gas exhaust. But by TNG some seven decades later, cloaked ships were completely undetectable again. The Mirror Universe Klingons had cloaks in "Crossover" but none in "The Emperor's New Cloak." And so on.
The only way it makes sense is if you assume that cloaking devices aren't one technology but many. Logically, there would be an ongoing arms race between stealth and detection, just like in real life. Every time a new stealth technology is developed, eventually new detection methods are devised to penetrate it, and that particular type of cloak becomes obsolete, but then a different cloaking approach is devised to block the new detection methods, and it goes back and forth and back and forth. Not only does that resolve the inconsistencies, but it just plain makes sense in its own right. It would actually be completely nonsensical for all cloaking devices over the course of centuries to be the exact same unchanging technology, because
of course everyone would be constantly inventing new ways to pierce cloaks.
By the time DS9 and Voyager came around, there was a greater appreciation for "If a character says this, it effectively means we can't change it."
I'm bewildered by the assumption that just because a character says something, that means it must be taken as absolutely accurate and truthful. That's completely unrealistic. People are fallible. They make mistakes. They misstate things, they misremember things, they get things wrong, and sometimes they intentionally lie. There's a reason hearsay isn't admissible as evidence in court. What a person says doesn't prove anything except what they
believe to be true, or what they want to convince their listeners is true. Without external corroboration, there's no guarantee that a personal anecdote or assertion is accurate or even honest.
So people who are concerned with fictional continuity make things far too hard on themselves by assuming that every single spoken word
must be absolutely accurate. A lot of continuity errors are easy to brush off if you just assume they're misstatements or errors on the part of the speakers. And it's simply more realistic to allow fictional characters to be as fallible as real people are.
I can't help but use the Picard line about first contact with the Klingons. It was a throwaway line that became enmeshed in "canon" and stood in the way of telling several very good stories.
No, it didn't. On the contrary -- the makers of ENT totally ignored it and did what they wanted with the Klingons anyway. Fandom has this warped, deluded notion that "canon" is some kind of holy law imposed on the creators and tying their hands. That's totally backward and ridiculous. Canon is just a word for the stories the creators tell. They are the ones who dictate what canon does, not the other way around. The creators of fictional canons have always been and will always be perfectly free to rewrite their own universes as completely as they want -- like when the makers of
Dallas retconned a whole season into a dream just so they could bring one character back from the dead when the actor agreed to return. Or like when Marvel had John Byrne give Spider-Man a new, "updated" origin story that was meant to be a canonical replacement for the original one, but it turned out so badly that later writers just quietly ignored it and went back to the old canon. The creators of canon decide what bits of old canon they want to keep and what bits they want to discard. What they create
is the canon by definition, automatically, no matter what they do. And new canon overwrites old canon all the time.
The only people who are actually restricted by canon are people like me, writers of licensed tie-ins. We're just borrowing other people's toys, so we have to put them back the way we found them. But the people who own the toys can modify or reassemble them however they want. It's not history, just make-believe, so it can be changed.
The truth is, Enterprise's continuity isn't much worse than the other Treks, it's just magnified because people were unsatisfied with the show overall and continuity seemed an easy target.
It wasn't even that, really. The fact is,
every new incarnation of Trek has garnered the exact same complaints and criticisms. Go back to the early '80s and you can find fan letters denouncing TMP and TWOK in exactly the same terms used to denounce ENT in the 2000s and the Kelvin films in the 2010s. A lot of fans -- and TOS actors -- didn't accept TNG as "real"
Star Trek for
years after it premiered; it wasn't fully accepted until "The Best of Both Worlds" happened and blew everyone away. So it's just some people's kneejerk rejection of anything new and different. Sure, the quality of the work can help overcome those objections for many people, but there are some who will never let go of their intolerance for change.