Conclusion: We really like FATES, but lie to ourselves.

[Shurrikhan]

In terms of variety, we ultimately need to consider how spontaneous quests can manifest:
- Kill X
- Fetch Y
- Go to Z
- Defend Q

Honestly, these seem sufficient to do a ton of interesting stuff.

The issue is ultimately the shape of the encounter and the available responses* to threats or timers. That's where your emergent gameplay forms, after all.
* (Available here refers to "competitive" or "(near enough to) optimal", rather than just technically possible.)

For instance, let's take a "Savage" version of the initial Worms fate in South Thanalan. The objective would be Defend X (the civilians). But consider all that could go along with that:

• You have a finite number of NPC guards to aid you.
• You have a finite number of defensive structures.
• You have a finite number of provided items (e.g. explosives), though perhaps you could have crafters make more through FATE-specific crafts (hit interact with the glowing desk and have at it).
• You can command the NPC guards to charge, pull-back, etc.
• You can have use crafted items (beams, stones, etc.) to shore up defenses.
• You can pull back K.O.'ed guards to where they can be resuscitated.
• There can be 'sapper' worms who borrow deeper into the town.
• There are a limited number of elite worms, with their own triggers, including worm death total, worm death rate, guard death total, guard death rate, civilian death total, civilian death rate, explosives use total, explosives consumed (and stockpile seen), a particular other elite worm attacked, a particular other elite worm killed, etc., etc.
• You can have NPC civilians feign death (e.g. hide in the basement of a building that is destroyed), including to trigger elite worm spawns (into traps), so long as you can get them out in time (before they suffocate or are noticed by sapper worms).
• There is technically a finite number of worms, but more importantly their is a scaling rate of their being brought against you based on the elite worms, though worm holes (not wormholes) in the area.
• Rate of kills can scare back worms, offering temporary reprieve.
• You can exit the immediate FATE area to any of the connected FATE areas, e.g. to attack an elite worm directly (offering distraction mid-assault or denying the worms an opportunity that would eventually overwhelm you) or to bomb worm holes (more effective in getting initial kills, as you're collapsing entire tunnels, and --if you can close a whole network-- reducing their incoming numbers, than simply defending against them).
• Etc., etc.

Voila. You've got the most complex and ingenuity-enticing fight in XIV. In a FATE.

It's all about the doodads, units, mechanics, etc., more so than any general objective type. The four basic objectives are wholly sufficient. The devs have just barely scratched the surface of what all can be done with them.