Whilst I appreciate the idea of this to a great degree and think it would be a great addition to the story element (not story mode specifically, but just to enhance the idea that certain characters have “beef” with each other), there is one overarching accessibility related question that ties into all this:
Would we still have sounds/voices to accompany the body language of the characters that don’t necessarily speak? If we take, say, Aganos and Kan-Ra:
Kan-Ra: So it has come to this. I’ll give you one chance to turn and walk away.
Aganos: (raises a fist and moves into a fighting stance, throwing a rock to the floor or similar to show he’s not backing down)
Kan-Ra: Fine then. But it is your funeral.
With Aganos, he has sounds/vocalisations associated with his various movements and I believe moments like his response to Kan-Ra could be well executed if done correctly.
Furthermore, if we take Fulgore VS TJ:
TJ: Time for me to show UltraTech that skill wins over technology.
Fulgore (in the long drawn out syllables from the trailler reveal way back when): Fulgore defeat TJ. (stamps twice on the ground, once with each foot, raising a fist just before the stamp so he ends up in a fighting stance)
TJ: Oh really? Seems you want yo ■■■ kicked real bad. Bring it!
That last line was a deliberate use of Jax’s line from MKX, as he does, in a few of his intro dialogues, reveal his distain at people “stealin my lines” or similar. It’d be good I think to have this as a reference to the fact that KI appeared to borrow so much from what surrounded it back in the day and still, to a greater or lesser extent does to this day.
Moreover, I believe that if this is done, they should be skippable as in MKX, or it could be an option that the player can turn off/on maybe? Also, whoever said variation should be a thing is definitely right. With MKX far too much of the time in that game the dialogues start with just a character’s name, which can just get down right frustrating considering the delivery/quality of some of the lines/sequences is far improved at times.
All in all, I like the idea and would like to see it worked on in the future. Part of what makes story mode from S1 and s2 (the latter in particular) for players with no vision whatsoever so bland is the seeming lack of anything going on during loading. Moreover, the rival fights lose their impact when just voiced by a narrator beforehand. I’d kind of hoped IG would’ve realised this and tried to make it similar to Tekken, where there’s a cutscene before and after the fight at the very least to solve one of the two problems, but of course they didn’t think to use the characters voice actors that were so well thought through in the traillers 
.
I@m not saying my opinion is the only one, I understand that dialogues can get rather frustrating at times etc, but I think if examined carefully enough it could be well executed. For those characters that don’t speak at all, you shouldn’t need subtitles really as if you can’t see it, the voice/vocalisations can express emotion just as well as body language can (even if it’s easy to misinterpret).