What if we don't actually kill him. In fact, when I think about it, it would be a bit weird for the game to have a different warchief at some point. They would either have to use phases to make it work, or it will feel weird to have a certain warchief greeting you in Orgrimmar at level 1, and then having so much story about Garrosh in the zones, even up to Pandaria. Sure, technically that is in the past, but will they then only make you see the new warchief in Orgrimmar when you're 90? Or 91-95? What will happen when patch 5.4 releases, will Garrosh still stand around in Orgrimmar?
Replacing leaders in the game is difficult.
And because of that, very often when characters die, it is not reflected in the game, like with Jaina and Rhonin, or Korialstrasz. The only time they really changed around the leadership of a lot of races was when Cataclysm launched. Cairne died and was replaced by Baine, Magni was turned into diamond and was replaced by the council, Thrall left and was replaced by Garrosh. And that was really only possible because they've redone the world. They've also replaced Anduin/Bolvar with Varian before Cata, but there weren't so many problems with that lorewise. There wasn't so much tied to the Stormwind leadership. It's a bit different with Garrosh. The Cataclysm and MoP storyline seems to be heavily focussed on Garrosh.
Can this change in leadership be done without feeling strange?