Oof. That'd depend a lot on what is permitted.

For instance, if no holds were barred and it was just the 'open world repeatable content' niche I needed to hold onto, I'd probably scrap almost everything to do with FATEs in favor of dynamic forces moving around the maps.

Sticking to something more reasonable, though, and skipping the obvious like "Better scaling!", "Being able to receive whatever rewards you've earned thus far on a FATE even if you've gone into an instance or to another zone by the time it completes!", or "Rewards reasonable enough to still bother doing them after unlocking each zone's full rewards!", it mostly comes down to (1) minor gameplay and thematic components, (2) more interFATE interactions or series, and perhaps (3) higher difficulty tier of FATEs.

Though I can provide examples of the first two if needed, only the last needs much explanation:
Imagine an extension of "Better scaling" to the point of scaling encounters specifically for item level and the number of players in each role while also taking into account party damage dealt on a similar step in an earlier FATE in the given series, and rewards increasing the higher (i.e. harder) you scale it. If you have 3 tanks, 3 healers, and 2 DPS, for whatever reason, DPS checks will be softer, but you can damn well assume every one of those tanks and healers will be needed and will be under considerable pressure. The fight might start off with a horde of adds and two mini-bosses each with buff auras that must therefore be tanked away from the rest, with another mini-boss or add wave spawning after just enough time by which it'd be expected that you all (according to your DPS from the previous FATE) could finish everything off when accounting for movement, gathering, and swap times. By the end of the fight, each of these interactions (the manner of healing, tanking, and DPS-check responsibilities) should be swapped out, but the pressure should always remain, even if, say, 'separate tanking' ultimately becomes 'swapping in for incredibly frequent tankbusters' against a single, final boss, etc...
:: Not that this is ever anything but a false ultimatum, but if I somehow had to choose between getting people to play FATEs through making FATEs themselves more interesting or just upping their rewards, I'd go for the prior every time. Sadly, apart from the option of a single Duty Action, FATEs are limited to, well, the same toolkits as any other form of combat, which at this point don't allow for all that many interactions (especially compared to, say, a HW or SB-era Ninja or early ARR-era Bard, etc).