If you have a quest or Hunt bill that requires a specific FATE, that FATE will then not spawn for 3+ hours.... where as if you don't require it, it will always spawn frequently (Giant Seps I'm looking at you ><). Maybe the enemy senses your bloodlust.... or maybe they're just psychic.

A quest or FATE title will always have a punny name taken from a TV show/film/game/anime/manga/cartoon/comic/novel/song/band name/some other element of pop culture or a figure of speech. No exceptions.