I personally don't think that's true. In fact, you'd think that something as comparatively short as a fighting game story wouldn't strain the writers.
Characters only fighting one-on-one isn't really an issue people have with the games' story, is it? Cause if I remember right, the problem people take with it is that the characters are reduced to caricatures.
Is that a side-effect of a shorter story? Regression?
Neither of these. You'll notice that none of the Persona 3 cast members are reduced to mere caricatures. Except perhaps Akihiko in Chie's joke ending but again that's the problem with trying to force ArcSys's story structure on a series that never had joke endings like that before.
The biggest problem with Persona 4 Arena is that it's trying to continue off Persona 4, and Persona 4 was the most self-contained entry in the franchise. Almost nothing connects it with previous installments. You have the Igor, the Velvet Room, a few funny cameos, Margaret's sidequest in New Game Plus mode, and that's about it. Most of those are elements that appear in every installment. To make matters worse, the true ending basically wraps everything up. No questions are left unanswered and nothing about the particular story is still open. Persona 4 Golden even went a step further with it's bonus epilogue. This isn't bad in regards to Persona 4 itself; it's a murder mystery, and it wouldn't be very interesting or well written if details were left hanging, would it?
This however presents them a problem with Persona 4 Arena and Ultimax.
They have nowhere they can go without compromising on the true ending to Persona 4. This is why we have Yukiko's story mode in the first game being absolutely boring, and why Kanji does practically nothing in either game. And then you throw the fighting game story structure on top of it, effectively enforcing that the story MUST focus on a character to some degree. Otherwise, there's no reason to play as that character. There's just not a whole lot of room to write stuff, really.
On the flipside, Persona 3's story is absolutely loaded with details. It's continuing off a major plotline started in the first Persona, the ending doesn't answer all the questions (hence why we got FES in the first place), and there were incredible amounts side stuff they didn't even use. This shows too: The entire plotline of the first Arena game is basically continuing off the stories started in in the drama CDs. Ultimax is no slouch either here; Several side characters from Persona 3 return or are re-introduced in new roles. They didn't even run out of stuff to work with either. Yuichiro Tanaka teases the possibility of seeing a sixth generation Anti Shadow Weapon in the first Arena artbook. Not to mention the plotline with Elizabeth, which they seem to want to continue on for the foreseeable future.
Put simply, the writers wrote themselves into a corner with the Persona 4 cast. I don't think they intended the game to get as popular as it did. Unfortunately, this means they little room to work with. Add the genre change on top that Flux went into significant detail over above... and yeah. It's a wonder the story is as good as it is.
There's no need to develop characters that are already developed. But it would be nice if they stayed at the point they had developed to. As for needing to have fights dispersed frequently enough, Labrys and [Redacted]'s chapters pretty much prove that's not an issue. Story mode is for story foremost. If players just wanted some fluff in between matches, they'd pick Arcade mode, wouldn't they?
If Labrys's story and [Redacted]'s story were the entire game, the gameplay would get boring
real fast. If you wanna see a fantastic case of this in action, go play the original Melty Blood story mode to the end. The one fight in Labrys's story mode only exists just as a warmup after having gone through an hour or more of story without any gameplay at all.