Clearly you know nothing about the art of game design, so I'll educate you.
Simply put, they add
flavor and
variety. Things like class-specific (and even race-specific) content do nothing but add
value to a game. Even if it's only 10 or 15 quests spread out over 80 levels, it keeps a player interested, because in their mind they're seeing content specifically made for them ("oh shit, the Silver Hand suspects demons are masquerading as fellow paladins?? what can I do to help?" or "Garrosh wants to know what Sylvanas is really up to, but he won't trust anyone but a fellow orc." (the latter could also be interesting if it were only made available upon honored/revered rep, but I digress) ). And if the stories are well-composed and compelling enough, maybe they'll want to see what the stories are for the rest of the classes and/or races (which, in business terms means they play more and they play longer, and as a result, the business makes more money).
(Additionally, as an ancillary benefit, it would also work towards preventing those who like to reroll new toons from wanting to gouge their eyes out from the sheer amount of linearity the current incarnation of quest flow practically forces...)
Although, seeing as you have such a big problem with any quests that are specific to a certain class, I suppose you also share the same distaste for racial starting zones, and maybe even Horde- and Alliance-specific quests as well, seeing as how they prevent half of the player-base from experiencing the content and all (the horror!). Perhaps we should just reshape the world - again - and instead of continents and zones, just make it one giant sandbox (literally). We'll make every new character spawn in the exact same location, regardless of affiliation (in fact, why not just get rid of all affiliations whatsoever), and have access to all the same groups of quests. After all, that's the most efficient way to design a game, right...
In closing, it's a very good model for an MMORPG. It seems you're looking for something, though, that questing just doesn't provide. (Seeing as how
all (non-repeatable) quests can only be consumed once per character, proper class-specific quests would be no different as every class would have them.)
Maybe an MMO
RPG just isn't for you. (and there's nothing wrong with that) *shrug*