Every time I play a modern Final Fantasy and watch a cutscene, I have a tendency to reimagine what the game would look like if it were done as a 16-bit game, FFIV-style. It's probably the nostalgic in me, but it also helps rationalize some of the completely ridiculous things that happen in this game. (Ditto FFX.)
When people talk about the Uncanny Valley, they're usually referring to visuals, but the same thing applies to narrative too. When you have squat 16x16 sprites doing ridiculous things, it's OK, because they're 16x16 sprites - there's a huge layer of abstraction between the player and the game. That's why they can address the player, per below, and not seem extremely stupid.
Think of the one scenes in the beginning when Snow and his jailbait (??) fiancee are stupidly flying around the fireworks, then get all surprised when they almost get killed. Couldn't you imagine that scene being kinda funny if it were done in a 16-bit game? Here, it's just kinda facepalmy. On the opposing side, think of that one scene in Final Fantasy V where Bartz and Galuf sneak up on Faris sleeping and then notice how attracted they are to her. The way it's portrayed - the funny little hoppy expressions, the little heart emoticons - pretty humorous! But imagine how it would be played out FFXIII-style, with full motion computer generated cutscenes, complete with unnecessarily extraneous dialogue and hyperbolic body language. Ugh.
To put it in another, less theoretical context, and in another medium - think of the sex scene from Watchmen. In the comic, it was maybe a page or two, with the final part where they lean on a button and set off a flamethrower in a ridiculous visual metaphor, confined to a single panel. Even at worst, you can shrug it off. When you have actual real life naked actors doing this, complete with music, and actual special effects relished on this moment...yeah, wow, does it not work.
There's a special instance with Vanille. Here we have a girl so genki (I'm sorry for using Japanese, but there is literally no single English word that describes this kind of chirpy, upbeat obnoxiousness) that, despite all of the death and destruction going on mere feet from here, she's giggling and skipping and is all like, hey, Hope, let's go follow that guy that didn't really kill your mother for some reason so you can tell him off! (Which I think is why they're both involved in the plot at this point? I'm not entirely sure.) My roommate insists that Vanille must have some kind of Terrible Secret, or at least brain damage, that will eventually explain her mannerisms. I don't quite share that optimism.
JRPGs have always required some level of suspension of disbelief - in FFXIII's case, you just have to accept that this is a world where blue-haired J-rock stars and the world's most fashionable hobo are qualified to lead a resistance movement. But where do you draw the line? As much as the game's opening segments are intentionally obscured by inexplicable jargon whose meaning isn't explained for a few hours, it's this kind of technicality, this kind of flair, that gives the JRPG its unique voice, however ridiculous it may be. Like mentioned previously when I was talking about No More Heroes 2, it's a fine line to walk, and with other Western games being able to come across far less embarrassingly, it's something that the developers need to be consciously aware of.
And it's not like the developers are completely absent-minded, either! According to this interview, director Motomu Toriyama acknowledges that, when you have a fully 3D world and realistic characters, it looks pretty ridiculous to have combatants line in a row and take turns swatting at each other, which is why the system in FFXIII is more actiony. And he's right! Now they need to apply that logic to the narrative, and we should be good to go. It's not like they haven't before - Final Fantasy XII was downright classy in comparison - but that's one of the sad things that went out the door in the name of reinvention.