A few ideas I had just as I've been doing the fates:

1. Playing off the original relic quest a bit: EXPLORE the Diadem for your weapon's components. Maybe it's in the caves. Maybe it's in a buried coffer. It's DEFINITELY there, but you have to find the pieces to have it constructed. This would encourage more than the usual dino-zerg, and introduce actual exploration to the Diadem.

2. Regional/Lore-based logic: White Mage? Run the Amdapor instances to find your relic piece. Machinist? Infiltrate a Castrum for Magitek components. Paladin? Perhaps your relic piece could be buried within the Sunken Temple of Qarn, or one of the many Sil'dihn/Belahdian ruins in the open world? Something different and INTERESTING for everyone.

3. Playing off the Last Ones mechanic in Lightning Returns: A bit grindy, but not FATE oriented; players are given a set target within different areas and through eliminating more and more of that type of creature, you give rise to a demi-primal of sorts. Essentially, you'd create an NM that successfully defeating awards you with the "soul" of said creature within your weapon.

Most if not all of these ideas are half-formed, but would still be at least more interesting than Atma 3.0, dungeon bucket list, and component/craft grind.