Why is time of day nearly meaningless in WoW? A very few things will change from day to night, which I must now admit I cannot even remember. Darkness changes nothing, except to cause me to constantly sit higher up in my chair, attempting to take advantage of the change in brightness based on the angle of my monitor. Incidentally, I had this same problem in Minecraft, except constantly, until I finally just gave up on conserving torches.
A world with relevant time of day could be much more in depth and interesting. Want to raid a city? More guards sleep during the night and they can't see quite as far. They'll be woken of course, but if you can start out with an easier fight, that helps. At night many animals and people will sleep. But more undead may awaken along with nocturnal animals. Adventures may be easier or higher depending on time of day, but none will be trivial or impossible.
This is an easier mechanic to work with in a single-player game. Wait or sleep mechanics can allow a player to skip to the time they need, something which I cannot see a simple solution to in a multiplayer world. Even if there are not these mechanics, the particular time isn't such a problem, since there are many activities to do, all ready to be picked. In contrast WoW has a narrower band of relevant content and the social aspect means that people will want to do a particular activity. It would be awful if late night raiding guilds never got to do Sunwell because it closes after 10pm. Similarly, raiding Naxxramas at noon when all the bosses are napping would be terribly boring.
I see two ways around these problems.
First, don't directly link game and real time. Make game time run at a different rate, such that a player logging in at the same time each day will be able to see each section of the day, so that if the day is only night and day, then every other day there would be a full cycle, while night, dawn, day, and dusk cycle would repeat over four days. I do not meant that each aspect would take a day, though slowing down time could work. Instead time would go faster, such that in a four-phase day over a four day cycle a 24 hour period of real time would cause a 30 hour passing in the game, so that if you always log in at 18, then you will see game times of 18, 24/0, 6, and then 12, before the cycle starts over again at 18.
Second, players could use some sort of mildly expensive reagent and cooldown to create a time bubble, allowing them to run instanced content in a more suitable time, or possibly even triggered a phase change for outdoor content. The idea here is to offset the potential irritation of being unable to play due to relative time of day, without making game time meaningless.
The changes due to time do not need to be very big. It is probably best that they are not, since too dramatic of a change could tip the balance from immersive to annoying. For example, in Oblivion there is a fence who sleeps at day and hangs out at an inn at night. His house is close to the inn, so that the difference in convenience is maybe 30 seconds of running. But it helps to establish that day and night are different. If I arrive in town at night, I go to the inn, while at day I go to his house.
But if the changes were significant enough, even that could add to the fun. If I arrive somewhere and everyone is asleep, I could buy a room for the night to pass the time. Or, I could rob some houses under cover of darkness. Limitations can spawn creativity.
Unfortunately the loot-focused nature of WoW puts a lot of limits on the possibilities. We become very goal-oriented, with the experience often being little more than a barrier. With this perspective, fighting the Day Dragon isn't a novel change from the usual attack on the dragon lair at night, in which we'd fight the Night Dragon, instead it just means we're fighting a boss that doesn't drop the loot we want. Or more dramatically, if during the day all the dragons are off flying, making this a great time to steal dragon eggs for gold and cooking, we're going to be annoyed that we can't fight the actual dragons for loot.
I don't think a dynamic world can coexist with a focus on loot acquisition. Maybe I'm wrong.