Having to do that quest over and over again will result in either of these:
a) Player keeps playing until he has every mog weapon, which is delayed greatly by the annoying quest, then proceeds to take a break from the game since he finished all endgame-ish content.
b) Player gets sick of having to do that annoying quest over and over again and stops playing before getting all mog weapons. He could tell SE was using a cheap trick to try and trick him into playing more so he is less likely to return.
Sure they would get the fanboys to stay interested in the game longer, but at the cost of their other players which are the majority.
SE needs to face the fact that most of their current and potential customers are not OCD and have lots of alternatives when it comes to having fun.