Dungeons do not need to give more experience than what they give.

The problem here is the FATEs, not the dungeons. The FATEs need to be nerfed in some way. I think the best way to nerf FATEs is to reduce their spawn time so that there is always a 3 to 5 minute gap minimum between the appearance of one in each zone, which would also make them more interesting when one one pops up. I'm not referring to the spawn time between a specific FATE, but rather the period between the spawning of any 2 FATEs in a zone. In example FATE A spawns at 1:02, then at 1:07 FATE B spawns, which is obviously a different FATE than FATE A. This would be better than an experience nerf.

Experience nerf on FATEs would be bad because then no one would have a reason to play them unless it's the ones that actually give something more than experience. Doing the nerfed spawn time way, but keeping same experience, would be better since people will still want to do one when it appears for it's great exp boost to add to whatever else they're doing to get exp, while making dungeons more viable again, and fixing the fact that leveling is currently too fast.