This system sticks out like a sore thumb from the rest of the relatively progressive and rewarding game design present in the rest of FFXIV. Apparently, though I was not one myself, 1.0 players report that a token system was eventually put in place meaning that all fights - even ones where you did not directly receive a weapon drop - contributed towards this final goal. I would recommend either limiting the drop pool to only such jobs which are in the instance (you cannot add members midway through so this cannot be abused), or even better implement a token system which guarantees the drop after x number of kills, probably around the 5-10 mark.

It would be a shame for the game to be marred by such a poor choice of loot system, especially since this is one of the first thing many players are going to see once they hit 50 endgame levels and have to make a decision about whether to keep playing the game or not.