Phasing is a potentially significant advance for storytelling in MMOs, because it allows the world to evolve around you without breaking it for others, so Blizzard are to be congratulated for exploring the idea in WOW. It's been used to good effect in the post-Cataclysm Silverpine Forest, where the Forsaken are locked in an evolving war against the Worgen. From an individual's perspective, it looks much like a single-player RPG. And that's the problem...
Fundamentally, MMOs are not single-player games. They aren't ever going to do as good a job on that front as the genuine article, because they have so many other constraints on them. Turning an MMO into a pseudo-single-player game means that not everybody is in the same reality at once, which starts to gnaw away at that feeling of being in a virtual world. That's already been eroded to quite an extent through the use of instances and dungeon finder and this is one step further.
Let me give you a concrete example. Yesterday, I needed to level herbalism on one of my alts, so I went to Silverpine, which was the appropriate level zone. I was pleasantly surprised by how few other people were there and managed to gather many herbs quickly. Why was the zone so empty, when it's such good fun? Well, it wasn't of course. There were many people there, each occupying different phases of the zone, so they never interacted. If you've never done the Silverpine quests, you can quite happily wander around in this alternate reality picking herbs to your heart's content. It's easy, but it's hardly challenging and it's barely an MMO at all.
At their core, MMOs are about interacting with other people and we tamper with that at our peril. It might make for some nicely plotted solo quests, but I'm not sure it's worth the price.