Should Moogle Treasure Trove be Permanent?

[Kaurhz]

Yes, it should be a permanent thing, and the rewards/duties should be cycled, and additionally they should have more substantial rewards included.

Treasure Trove provides some good replayability for a few people.

[Rilifane]

Yes, it should be a permanent thing, and the rewards/duties should be cycled, and additionally they should have more substantial rewards included.

Treasure Trove provides some good replayability for a few people.

That is pretty much what Trading Post is and probably what Atelier is suggesting.
I like the system. After earning the maximum amount of points through various things for the month, you get a substential extra reward like a full set of tmog, mount, pet etc. which can even be from the Blizzard Store. It cycles through rewards so it's not a FOMO system. The activities include a lot of non-combat stuff as well, mainly since there is no pressing need to fill duties. I'd learn more towards party-based battle content for FFXIV, though.

For Treasure Trove, they could make it so once you earned a certain amount of tomes per month, you get a special extra reward in addition to being able to buy some of the monthly rewards. Even if someone no-lifes it in the first week, at least they had something rewarding to in that first week? It also keeps it rewarding month after month, depending on how important the extra reward is for you.
Activities should definitely cycle as well, including other things than dungeons/ alli raids would also be nice like OP suggested. FATEs, Deep Dungeon floors, Bozja/ Eureka stuff can all work as an option as long as the amount of tomes earned reflects the time spent.