Since the Masked Carnival came out we've seen renewed calls for some implementation of the special-condition and time attack challenges on normal content. Random shower thought on how that might look:
1) Transform the min ilvl sync option into the "challenge mode" option. Selecting this option syncs you down to the minimum ilvl, disables echo and (on the backend) turns on the kind of action/event tracking they have in the Carnival.
2) On some sort of schedule, have a list of accumulating and/or rotating challenges for players to complete. These could be as simple as 'clear x in y time' or 'clear x with no deaths', or more wacky like some of the BLU challenges are.
3) As for rewards, I propose clusters for grade VII materia, coupled with making them not otherwise as common as grade VI are. Rewards would scale with challenge difficulty, so you could just always have a 'freebie' or two like a no-death dungeon run each week (and/or other limited means of procuring it) so that everyone can get materia over time. Just those with more ambition might be able to get five or eight a week or whatever.
Obviously lots of details could vary, but the core point is that something like this is readily possible. If SE can do the Carinval stuff, they can absolutely do this, they'd just need to find a good answer for what the structure / rewards would be.
Just to be fanciful, imagine if there were a board with a list of challenges available, some weekly, some monthly or even patch-long. And then four weeks after 4.5 the board looks like:
(note these all would be min sync / no-echo and my times are largely made up)
-- Expires 2/11 (weekly)
(1 cluster) Clear Gimlyt Dark in under 15 minutes
(1) Clear Sohr Kai with no deaths
(1) Clear The Whorleater (Hard) without killing any of the Sahagin adds
(2) Clear Kugane Castle under special conditions (*challenge mode causes certain mystery alterations this week)
(3) Clear The Wreath of Snakes (Extreme) with no deaths
-- Expires 3/5 (monthly)
(5) Clear Orbonne Monastery with no deaths
(5) Clear Alphascape v4.0 (Savage) in under 10 minutes
-- Expires 5/7 (quarterly or something)
(10) Clear The Burden of the Father (Savage) with no deaths