YES fates are broken.

[Memento]

Yes waiting three hours for a fate which could of been best spent elsewhere is clearly working as intended.
And way to go taking it off topic, this post has nothing to do with coil

No one told you you had to do Animus. You knew what the requirements were and what might happen (including rare FATES.) If that wasn't something you were on board with why sign up? There are plenty of other weapon alternatives for those that don't have the time or the will to fulfill the relic weapon requirements.

[Tsunenori]

No one told you you had to do Animus.

The problem that people have with this is that it's a system that encourages you to wait around doing almost nothing in order to get something you want, rather than keeping you engaged for a long period of time. It wasn't realistic on my server to do other FATEs while waiting for book FATEs to spawn, because the FATE you wanted would be finished by the time you made it back. A decent amount of my Scholar Animus was done alt tabbed playing Minecraft or Hearthstone on a second monitor, and that's not something that's necessarily positive.

Still, I think Taste of Fear might be the one FATE that was overlooked in their little balance pass a bit ago. Even Taken felt like it spawned faster than Taste of Fear.

[StarHate]

No one told you you had to do Animus. You knew what the requirements were and what might happen (including rare FATES.) If that wasn't something you were on board with why sign up? There are plenty of other weapon alternatives for those that don't have the time or the will to fulfill the relic weapon requirements.

You seem to be missing the entire point. In the last couple patches they changed it so that the longer it has been since a fate spawned, the more likely it is to spawn. If you are clearing the area, no single fate should take longer than 3 hours to spawn. The OP is saying that isn't happening as she waited for more than 3 hours clearing fates and it didn't pop. Wanting or not wanting to do her animus has 0 correlation with the change they made to fates not working.

edit - I went and checked, it is the 2.3 patch notes: "The chance of a FATE occurring will increase the more time passes since its last occurrence, increasing the overall frequency of FATEs."