The only advantage I can see to assigning all of your hits at once and rolling all the damage dice together is that you could use a single Grit to reroll any or all of the damage dice since it all occurred at the same time. But this could only be done when rolling damage for several hits all on the same monster, right? You could not be rolling 3 damage dice for three hits each on a separate monster and then still use a single Grit to reroll whatever damage results you didn't like, right? Otherwise, why would you ever assign hits/roll damage individually?
We allow assigning dice to multiple enemies at the same time, and just use different colored dice. All the rules say on this is that you must assign a hit (or group of hits) before rolling the associated damage.
It comes up very rarely though, as usually players want to be sure they kill something before moving on to the next target. I sometimes do it as a time-saving measure for area-of-effect stuff, like rolling dynamite damage for 2 or 3 models at a time.
Then, regardless of the answer to the questions above, when you assign hits together and then roll damage dice together (assumed for the benefit of being able to use one Grit to reroll any and all dice if wanted), if the damage assigned from hits to one monster is overkill so that you could have/should have split the hits up to more than one monster (which you would have done had you assigned hits/rolled for damage individually), you can't retroactively assign a hit and it's damage to a different monster, right?
That is correct; you cannot reassign overkill damage to another monster.