It greatly saddens me that the whole point for the so-called 'fetch quests' in the game is completely lost on most players in this thread - it's part of your job description as an adventurer! Back when you first started the game and signed up at the Adventurer's Guild, the guild proprietor actually tells you right then and there what you are in for - helping people with mundane tasks! And that "rarely will the work be of realm-shaking importance" (paraphrasing how Miounne stated it in Gridania), but that it was still important, as it helps build trust and rapport with the people of Eorzea, a people who have experienced a horrible cataclysm caused by foreign powers.
Even the much-maligned Titan-lead up questline had a method to it's madness - the reason you were being made to do all that running around was again to establish trust with the Company of Heroes, a mercenary force who were the only ones to defeat Titan previously, but they paid a huge price in blood to do so. Thus, this cocky adventurer who claimed to have taken down a Primal already comes up willing to take on Titan, of course they're going to be suspicious and not exactly willing to believe they could do it, and they especially did not want yet another life or mind lost to Titan on their conscience again. Actions speak louder than words after all. So it was a trust building exercise, to show you really did have the stamina and drive to do so, even after doing all that messing around getting food (and even if you failed, at least you would have had a nice 'final meal' beforehand!
).
After all, the Warrior of Light's altruism and willingness to help others in need regardless of how trivial their problem actually is the reason why no one believes the Syndicate's lies at the end of 2.55
- the Warrior of Light killing the Sultana? It just isn't possible, the person who helps those in need regardless of how hard or trivial it is? It's inconceivable to actually have done such a thing! It's clearly a Syndicate plot to discredit them and seize power for themselves! If we hadn't spent all that time fetching trivial things for people, and had just been some mercenary who happened to kill a few Primals and assorted Garleans, we would not have been given that same benefit of the doubt by the common people.
And even if you completely ignore the narrative reasons for fetch quests, they also have a gameplay function as to why they drag the story out - as they were designed to be the main method of gaining EXP. Instead of joining a party and level grinding on mobs over and over again for hours on end, you simply play through the main scenario and sidequests and gain exp that way. Of course this resulted in the main scenario having to be padded a bit with filler quests at times out of necessity, but even those ones are usually handled in a more humorous light (such as the aforementioned Titan quests, or the equally-maligned Moogle quests in Heavensward).
Really, if you come into this game expecting nothing but mindless battles and stomping through random environments without a care in the world, you will be disappointed - everything you do in here has a story-reason for doing so, cause and effect and all that. Always there is a reason why you're being sent into that Allagan ruin or Garlean fortress or abandoned mine. It's a FF game after all, and FF games are story-based RPGs, even the MMO titles like FFXI and XIV. How hard is it to understand that?