I'd try to fix the whole story of WoW if I could, but ain't nobody got time for that. Instead, I'm going to concentrate on the Siege of Orgrimmar, as it's currently the biggest possible offender I can think of.
STEP ONE: Identifying the Problem
The necessities of the MMO genre have damaged a fictional universe already damaged by the necessities of the RTS genre. Concession after concession gets made to accommodate both the lore and the gameplay, but it's always the lore that has to make the concession, and not the other way around.
Both playable factions were expected to run each dungeon and raid, so both playable factions had to be given reasons to do just that. The Horde were told they had to save Moira Bronzebeard to help Thrall's efforts to reach a peaceful accord with the Alliance via Ironforge, which is *slightly* more understandable than the Alliance being told they had to destroy the Scarlet Crusade despite the Crusade being a useful tool against the Forsaken.
The solution in this case is obvious: Different dungeons depending on your faction, that provides gear that might look different but is statistically identical. This even has the added benefit of getting players to roll the other faction to see how their half of the story plays out, instead of having everything be mirrored because it saves time.
Now let's apply this thinking to the Siege of Orgrimmar.
What we know so far is that Garrosh antagonises the rest of the Horde so much that they rebel against him, and that the Alliance are trying to take him down as well at the same time.
Now why the hell would they want to do that? The Alliance has a perfect chance to allow two groups full of people they want to see dead to weaken each other, then go after the survivors with fresh forces. Instead, they're wasting soldiers and resources helping the enemy they're at war with clean up their own internal problem, all on the off chance that the Horde won't seek to continue the war or be the ones to betray them just afterward.
Think back to the first sentence in this section. What does it mean? It means that in order for both factions to have a desire to do the same raid content, either one or both must be written like idiots at times. The community has always accepted this in the past, but I would argue that all factions MUST be self-serving and have their continued existence as one of their top priorities.
If taking part in a raid or dungeon goes against that faction's self-interest, then it either gets cut or it weakens the story.
This is even more important when said faction is actually a nation, rather than just a group of people brought together by a common cause who will then disband when they have no more reason to stick together. And it's even more important when said faction has been at war several times with the people they're now expected to help.
Sadly, the way this is doubtless going to play out is that both sides will fight the same bosses with the same mechanics at the same time and the victory will be referred to in future lore sources as being the work of "brave heroes" in order to never answer the question of who canonically did what to who. It's a fix, and a cop-out, and still doesn't address the real problem of trying to understand why the Alliance would care about orcs killing each other instead of them.
STEP TWO: Fixing the Problem
So now we have the Alliance being told to ignore everything the Horde has done to them, presumably by big-name characters who have little, if any, reason to trust the Horde at all.
How do we fix it? Simple. In fact, it's not just simple: It's genius. It's genius and it helps bring back some of the partisan feelings sorely missed in this era of mistaking "gameplay" and "balance" for one another.
First of all, a chronology of events as I would have them unfold:
1) Garrosh's policies and actions have finally incited open rebellion among the Horde.
2) The rebellion appeals for Alliance aid. The Alliance refuses.
3) The rebellion, with no other choice, takes the fight to Orgrimmar itself. They make it to Grommash Hold, and finally kill Garrosh.
4) The Alliance attempts to capitalise on the situation. Some want to dismantle the Horde as an organisation, others want to slaughter the orcs outright.
5) Weakened by their struggles, the surviving members of the rebellion intend to go out fighting--but Thrall and a number of other shaman call upon the elements to wreck the Alliance forces. A great tidal wave crushes the Alliance foot soldiers and their supply lines outside of Orgrimmar, and violent winds and hurricanes cut their aerial forces to shreds.
6) With victory no longer assured, Tyrande calls a retreat.
This plan has several benefits, which I will now outline:
1) It provides both factions with reasonable, believable reasons for their actions, and lowers the issues I have with the Siege from "the lore sucks and the bosses will be the same anyway" to "the bosses will be the same anyway," and that can only be a plus.
2) It provides both factions with understandable reasons to keep the war going instead of having Garrosh blamed as the sole reason for it and that now he's dead we can all get along better. The Alliance refused to help because they didn't want to throw away their own troops and resources helping the people they're at war with, and they saw a chance to come out on top. This is a reasonable thing to do if you're Alliance, and an honourless thing to do if you're Horde.
And let's face it, the Horde needs reasons to hate the Alliance that aren't so ham-fisted they make me laugh.
3) It provides Thrall with some much-needed ruthlessness--anything, really, to move him closer to his Warcraft 3 incarnation where his motivation was to do what he had to do to keep the people of the Horde safe. If I was doing the whole story over, using the Dragon Soul would have killed him, but meh.
4) If Tyrande is the commander in the Alliance version of the Siege--which she should be, given she's the closest thing to a military leader the Alliance has on Kalimdor as she's the former general of the Sentinels and thus would realistically know more about warfare than Varian does due to her former immortality--then it should go some way to undoing the pitiful characterisation Blizzard have dumped on her so far.
She went from a badass in Warcraft 3 to an inactivate peacemonger in Vanilla (The Tyrande I remember would probably have kicked Fandral in the face for questioning her authority. Then again, though, Fandral wouldn't have had a reason in the first place to disagree with a leader who would have been on the front lines shanking orcs in Ashenvale). The inactive part is visible with the other leaders, but then Cataclysm hit.
Cataclysm hit, and she went backwards. From the short story that portrayed her as an emotional wreck in a toxic relationship that was written as being a perfect one, to the "Hush, Tyrande" incident in the Well of Eternity dungeon, to her constant whining in Endtime, I thought things couldn't possibly get any worse.
And then they got worse with Mists, where Tyrande--the former general of an an army that fights its battles tactically and excels at ambushes, mind you--has to be lectured on not zerg rushing by Varian, a man who has only ever had Standard Fantasy Prince Sword Training and never actually had to fight for his life before he magically became blessed by Goldrinn because a troll said he was as fierce as Lo'gosh just because.
But that's another issue entirely, as is the issue of Garrosh's personality jumping all over the place, to the point where Blizzard had to hire an external writer in order to get them out of the hole they'd written themselves into (Since his primary purpose in each scene he's in seems to be to act contrary to absolutely everyone around him on absolutely every issue whatsoever).