When people make a party of 8 people and do fates they go by super fast. That means flying from spot to spot completing fates in basically under a minute. What if another tier of fates showed up at that point? That would provide an incentive for maximizing efficiency in endless combat modes.
If there were a counter or a gauge for the rate of completion within a certain timeframe, similar to the exp chain bonus for individual enemies, then another tier of more difficult fates could spawn with increased or additional rewards.
Imagine a boss fate spawning due to the efforts of people in a party rapidly handling all the smaller symptomatic fates in a region. Imagine that by defeating this boss everyone area wide would be affected by a temporary buff to material drop rate, or some sort of increased drop chance for exclusive materials, or even mounts as there's a precedent with Odin and Ixion. It might take further testing, but if there were tiers to that buff based on how fast the Boss was summoned and cleared then there'd be some striation based on player ability.