Rare Encounters (dangers or legends of Eorzea(!?)): with really rare spirits or mythical creatures like from those fisherman's tales
( mermaids, kraken, sirens, ghost ships, scylla, lochness monster, Ayia Napa) at specific lakes, or others sea and maybe in cave pools.
Weather Conditions: ( many possibilities! )
-when it "storms" players have a chance of catching rare Fish A
-when it "rains" Fish B can be captured.
-and when it's "night" fish C comes to the surface.
Fishing Rare Fishes & Wild Sea Life!: which are only able to be captured at certain weather conditions[related to Weather-Conditions].
An instance in which you have to catch a whale >(FF Style)< or (other types of bigger fish); with many other fishers to help with the task.
----- Great Ideas&Suggestions you've also got here and there as well Thsscks

[I've organized them to making them standout more, somewhat] , also thanks for complimenting "spirit encounters" it goes quite well together with post, you've definitely got some good thoughts and idea going. [an FF XIV version of them of course, SE Devs could work with them and fix them up however they want.] -----