They could if it was done right, but therein lays the rub. After this atrocity I can see Blizzard separating themselves from this recent BFA debacle and avoiding it, either indefinitely or for a hefty amount of time, but I also believe they’ll at least ride the wave until it is concluded (regardless of how satisfactory [or otherwise] it concludes).
From there, the past issues of H&A will be referenced and used to remind people (during above mentioned ‘uneasy terms vs more important big-bad’ phase) that yes, this is Warcraft, and yes, H&A never get along, and hey, remember that time a tree burned down and things started going crazy? Yeah, we don’t like each-other, and don’t you forget it.
Just like Warlords of Draenor was put on the backfoot, it does get referenced here and there even in the present, however minor. BFA will eventually get that treatment as well, because without one immeasurable ret-con or going back in time, the story will be part of the story and it won’t fade.
I also think that a lot of people who, at first, believed that Alliance vs Horde in center frame would be a ‘good thing’ will be disuaded a bit after this. Sure, there will be plenty who will still firmly believe it should be the way to go in a game that literally has “WAR” in its name, but after the way this went down and the general disappointment and splintering, more will probably prefer to sweep it under the rug and go back to something akin to past versions, where (yes) the factions do fight eachother, but it’s not front and center.
EDIT:
In short, I don’t see why they couldn’t do both.
I have always attributed PC’s similar to ‘mercenaries’ or ‘adventurers’. Sure, they also represent their faction, but with a massive lack of choice in the matter. For one expansion we’re marching together with the opposing faction to deal with X threat, in the next we’re fighting each-other, in the next we’re almost entirely at peace while dealing with Z threat, then in the next we’re just leaders of our own faction/class/garrison building ourselves to deal with Y threat, then we’re back to uneasy terms trying to unite against another big-bad, then we’re back to fighting each-other again as yet another big-bad looms on the horizon…
If players truly want choice, it doesn’t have to come with unique quests and checkboxes where you say Yes or No, resulting in the need to cater to both sides.
You could quite easily have said choices represented through content. Maybe I’d rather fight N’zoth rather than stomach more ‘not really war’, or maybe someone else is the opposite and wants to take it to the opposing faction, N’zoth be damned. Factions, reps, content-types (which don’t punish you for focusing on one over another and/or doesn’t require you to do ALL of them to reach the same point at the end) and voila, players choose without a need to splinter. It would also be a focal point for PvP content options.
It doesn’t always have to be “We fite X, now we fite you, but wait, better fite Y, then we fite you again… Until Z… After Z we fite you RL”.