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!

).