First off, didn't end up trying EVE. Couldn't get the 2-week trial to work, and I'm not paying for it.
To the topic, now....
Yeah, I agree that the quests in WoW, etc., don't actually give me what I'm looking for, because they are not part of a single main storyline. They're really just another way to gain XP/EQ.
I also agree that implementing something like this would not be easy. But, couldn't it be something like a class-based ultimate quest? Let's take WoW, for instance. With the main back theme of the whole game being about the ongoing hostilities between the Horde and Alliance, couldn't your new toon, along with all the mini-quests, etc., that help him gain levels and equipment, also have a series of mini-quests that ultimately lead to a single, major goal?
So, in other words, you can still have things like, "go retrieve this heirloom I just happened to leave behind when I fled my family farm like the sniveling coward that I am..." quests (ahem, sorry), and these would still serve their ultimate purposes: to enable achieving game play, leveling, and equipment improvement, especially solo.
But, you also have a whole series of mini-quests devoted to your Main Mission. So, you start off with some NPC saying something like, "You must help in the fight against the Shadow." Or whatever. And all the mini-quests in this series are part of something you work on all the way up. Then at 60 (or 70, or add more to this Main Mission as the level cap is increased, with stuff like, "I know you thought you were through, but it looks like the Shadow is craftier than we first thought." Or something like that). Anyway, then at 60, you finish with some major mini-quest, maybe even something you need help with.
In fact, now that I think about it, it might be kind of like the Epic Weapon quest series from EQ1, only the goal is not another piece of EQ, but a role-playing-esque way to feel like you are, as others so eloquently put it, affecting your world.
Plus, this Main Mission quest series could be different for each class, and even perhaps for each class/race combination.
It just doesn't seem that hard to implement (bearing in mind, of course, that I'm not a programmer

).
What do you all think?