Should Horde be able to group with Alliance?

Zoso has an interesting post on factions, in which he remarks that both Horde and Alliance often do exactly the same quest for some neutral faction like Argent Dawn or Cenarion Expedition. But they can't group to do it together.

When I'm playing Horde I often get annoyed at Alliance players pulling mobs that I just targeted from under my nose. That makes you assume some sort of inate Horde vs. Alliance enmity. But when I leveled up my human priest I noticed that for him too it was mostly Alliance players that got into his way. No wonder with Alliance outnumbering Horde, the likelihood that a random player is Alliance is simply higher. There is no natural enmity, the players behind Horde and Alliance are the same. Sometimes during leveling up to 70, with Horde again, I even managed to cooperate wordlessly with some Alliance player who quested in the same area. He pulled a boss mob, I helped him killing it, then he stuck around until the repop, I pulled, and he helped. Very nice.

On a PvE server Horde and Alliance is often frequenting the same neutral villages without getting into each others way. So why can't they group together? Why did I have to make an Alliance alt and transfer stuff in a complicated way via my wife's account and the neutral auction house whenever I want to buy something from the Alliance AH? World of Warcraft has grown, in both landmass and level range, and once the first rush of blood elves and draenei has passed, it will be hard to get a group together for low-level dungeons. Being able to invite people from the other faction would be a real help there.

Even PvP doesn't always have to be Alliance vs. Horde. In the arena system you can be paired against players of your own faction as well as "the enemy". And while Alterac Valley has a strong Alliance vs. Horde theme, the other battlegrounds are so bland and symmetrical that nobody would really notice if two Alliance groups fought each other there. Obviously that would cut down on waiting queues, which would be an advantage.

So what do you think, should the barrier between Horde and Alliance be lifted? Or is having two enemy sides essential for the World of Warcraft?