I don’t think so. Yes, they are on the same page on most things, but put orcs into conflict with a loa, for example, and you could have some nice drama where the trolls stand against them, not because they hate the orcs, but because they are fighting for what is theirs. Not to mention that orc politics can widely vary with its leader. You yourself mentioned Garrosh, and the troll-led rebellion against him was not that long ago.
I don’t think race has to matter at all for that. Indeed, I’d be all for divorcing the story of racial politics from the player’s character choice. If there is one thing about all this “you are the super special champion of Azeroth, Maw Walker, titanslayer”-stuff, it’s that there is no reason at all to treat you like a grunt that a king can order arond, just because you share his race. The old factions may continue, or fall apart as the story wills it, but the player doesn’t have to be tied to that level of politics at all.
The main story just isn’t about some soldier of the Horde/Alliance anymore, it’s about a few heroes.
And yes, if you want pvp that’s as loosely tied to the lore as it is now, you actually don’t need to have armies behind you. You need different teams of equals to band together with. Like the covenants, but hopefully with a bit more hostility between them. Which shouldn’t be too hard, if there are actually ideological differences to clash over, which is something the factions haven’t really had for a long time. And since we aren’t talking about armies, but powerful individuals, there is nothing wrong with newly creating these organizations on Azeroth. I actually had an idea along these lines quite some time ago with some bare-bones ideas about how such covenants could look:
And concerning future racial stories and conflicts… well, either the player is in a neutral role, ferreting out the evil manipulative cause of the conflict, like heroes in such situations tend to do… or they can just have the opportunity to choose a side that they like, if Blizz is still willing to give us two versions of the same story.
I don’t even think they would need more content for that than they are making for two factions. The content would just have to be about conflicts of a much smaller scale. We might not see specific tauren content apart from a few mentions here and there for years… but neither do we now, they just assume that tauren fans would be happy with general “Horde content” as well.