But that's kind of the problem. If these FATEs are really so fun, people WILL do them whether you give them a reward or not. And if they're not, then that's obviously not good either.
This is where you can see an incentive system starting to show signs of weakness: when you have content that people want to do, but you don't reward them for doing it. As important as anything else, successful games align player goals with enjoyable tasks. Narrow windows for completing content (especially in a game that will probably suffer from a lack of content, at least a little bit) suggest that the content is being managed poorly as a finite resource.
Ok, now we're going to get slash fiction of Wint x Kachi somehere... rule 34 and all...
Never confuse your inference as the listener for an implication of the speaker.
Good games are subjective like good food is subjective. You're not going to seriously tell me that there's not a psychological basis for why pizza is great and lutefisk is revolting. The thing about subjectivity is that, as subjects go, humans actually have a great deal in common.