I can see 2 solutions to accomplish an ease for us:

1) Whenever a FATE is chosen for a daily (or any) quest, the spawn rate will be generally increased for the time the FATE is flagged for a quest.
2) A mechanism where the open World is scanned and if at least 1 player stands in the zone of a FATE that's part of any quest, the spawn rate will be increased.

Option 2 might be too ressource hungry so maybe option 1 is easier to implement.

Best would be if no FATES would be used for any quests tho but I doubt we can change's SE's mindset about them because it makes production of new elements quite cheap and easy.