Why would the alliance being the aggressor bad for the game anyway? I mean, it doesn't have to end with Genn going full Garrosh, because that would be a stupid story arc.
But Legion already showed that he holds a huge grudge against the Horde and Sylvi especially, ignoring the orders of his King and losing a major military asset in addition to many soldiers just because of his need for vengeance. So why would it be so "out of character" that he (and maybe Jaina) convinces Anduin that going after the Horde is a good thing now that the Legion is no more? Both Jaina and Genn have reasons for revenge on the Horde, and Anduin is still young and stupid.