MMOs get that way, but then again, anything with four or five or six sequels gets that way, too.
I don't mean that in a literal sense; of course ARR wasn't the 'sequel' to 1.0, nor was Heavensward a 'sequel' to ARR. But, in the sense of storytelling (and counting 1.0 and ARR as 'the first story'), we are coming up to part five of our favorite summer blockbuster here. By the time I saw Terminator V (technically, Genisys?) I stopped really trying to make sense out of the story presented to me in the earlier films. Was it still fun to watch? Sure. Would I ever consider it an epic extension of the story presented in Terminator and T2? Never, ever, in a million years. /shrug
I've attempted to absorb the entire story pf FFXIV over the past couple months. Personally, I don't think there are too many places where it doesn't make sense, but that too could be subjective. I mean, Star Trek had replicators, which made no sense because just about every episode's problem could have been solved with replicators. This planet has no food? Replicate it. The medical supplies won't get there in time? Replicate them. Dilithium crystal burned out? Replicate one!
The love of the characters and overall story arc help us with our suspension of disbelief. I tend to have the same experience with FF.
There's definitely a hard stop when each xpac's MSQ comes to an end; sometimes you have to force yourself to remember that the the "Post-xpac" stories came months after the main MSQ was finished. When you hop directly from the end of one MSQ series to the start of the next, the story can seem silly or muddled. Especially when characters change their moods or focus or reasoning literally from one cutscene to the next.
'Filler story' can be subjectively enjoyed by many. For any series, episodes that deviate from the main lore ("monster / villian of the week") can sometimes be a nice break from the norm. Personally, I love all of the weird/comedic storylines, and I consider those 'filler' since they have no bearing on the main story arc.
Last thing to remember is that behind this art there is a for-profit business. Hiring better writers takes money, developing better stories takes time. If there were no deadlines nor profit goals involved, you'd see storylines on par with what the best authors of our day have to offer.
Further to that, there are restrictions on content because of the ESRB rating. Try to imagine something like Game of Thrones but during family hour on a broadcast network like CBS. No gore, no language, no sex, and very limited violence. It would have been a much, much different show, and the lore would have suffered for it, IMHO.
What we need is an M-rated MMO developed by a non-profit company with limitless resources and access to the best creative minds on the planet, who in turn will also work for free.
Take my money.