It would necessitate more lore focus on the Elves in order to explain why they've managed to scrape together enough resources to suddenly count as a faction. This distracts from currently existing playable races who have received next to no story attention in recent years. All of these neglected races happen to be Alliance side.
There would also have to be comparable focus on whatever race the Horde gets to share with the Alliance. All of this is time that would be better spent on the Worgen and the Draenei, two races I'd be excited to learn more about.
Indeed, what cast off Alliance race would the Horde get? Highborne? Joined the Alliance recently, there was a big song and dance about it. Dark Iron Dwarves? From recent stories, they are actually getting MORE loyal to the Alliance. Leper Gnomes...ok now that's just taking the piss. We can rule out Humans in any shape or form, even Alterac Humans, as Humans are the Alliance core. And you've got a screw loose if you even mention Worgen, let alone Draenei.
It would damage faction diversity. Don't give me the Pandaren excuse and say that since the Pandaren have been brought in, they may as well allow it for other race. Ghostcrawler's recent tweet clarified that they weren't keen on the concept of neutral races and only employed it with the Pandaren because they thought the Pandaren would be unusually popular with both factions and didn't want to deny either side the chance to play one. Blizzard wants the two factions to be as diverse as possible, and making the Elves cross-faction would severely undermine that. Also, once you make one race cross-faction (again the Pandaren are an exception) then the pressure to make the other races available will start to become overwhelming. Why not the Alliance player who wants to be Forsaken? Or the Horde player who wants to be a Draenei?
The alternative is the solution to give High Elves some new model in order to differentiate them from the Blood Elves. This very day Blizzard confirmed that the great model upgrade is a mere 25% complete. You really think Blizzard is going to devote precious art resources to this pet project? And even if they did do this, the High Elves and the Blood Elves are seen as the same race by the vast majority of WoW players. Individuals on both factions would instantly begin campaigning for access to the 'other' Elf model, as some will prefer it to the one their faction has.
The impact on player population has to be considered also. Despite people complaining about them, the Blood Elves are individually the most popular played Horde race. Giving this choice to the Alliance also will over time result in a burgeoning population of High Elves. Seeing High Elves, Night Elves and Blood Elves everywhere you turn is not going to be particularly healthy to the image of the game. One in every three players could easily be some kind of Elf by the end of it.
The impact on current Blood Elf players. This is an argument I've not deployed much, but I will here. Currently, Blood Elf players play in one of the few fantasy universes in which they are allied to the Orcs and other assorted 'monsters' rather than the Humans. Allowing Alliance players to play a Horde race will make that Horde race feel less Horde. You are willing to undermine their sense of identity within the Horde to play the same race Blue side.
And the public relations nightmare Blizzard will have to endure if they ever announced the High Elves. More Elves? Alliance get Horde race re-skin?Blizzard out of ideas!
Face it. This isn't about denying people what they want. It's about those people refusing to think about the potential consequences of what could happen if they get their way.