Oh come on... there are something like 4 plots for all films/books. All quests fall into a very small handful of types.
To eliminate fetch quests (as in any quest that requires you to gather, collect or otherwise bring together one or more characters or things and locations...) and you'd have little game. If you also can't have delivery quests... then there really isn't a lot left you can do, except "stick them with the pointy end" or watch cutscenes.
What makes a game good or bad is *how* the quests are done, the quality of the situations these tasks are a part of and their context. If you don't *always* spot that this is "yet another Fed-ex", then the writing is working. If not, then it may not...
Even when it is as obvious as the nose on your face that we are doing a fetch quest it can still be fun. The 'spear/banner/armour' quest for AOK, the 'bring me a gift for the solution to the trouble (cow/bracelet)' etc were still at their hearts a "fetch quest", but fitted into the story rather more elegantly than the most basic versions...
And of course the supremely dull/amusing/excellent/hilarious harpy quest... good, bad or indifferent according to your tastes... but 100% pure unadulterated fetchiness.