Without them, there would be one less way to get XP, and i really feel people would be doing more hunting logs, dungeons, perhaps farm groups in particular parts of the world with AEs (similar to standing in the Mines in Northern Thanalan while fate grinding/waiting for Dark Devices. I think Dungeons would be a higher priority as they would be the big XP makers after Hunting logs are exhausted. I think the rest of the world would be a bit more populated....
I also think if fates hadn't have been added they would have made quests repeatable by class. If there were no fates, the lack of questing for alts would lead to only dungeons, hunting log, AOE farming. Might have even been Experience Camps!!