Came up with this in IRC, was positively received

Quests should have a variety of extra triggers: such as tech researched

Example: if you have research leather armor, you could get a hunt beast quest- with a reward of beast hide armor of some sort for your champion

Expert Spellbooks might give you a fetch quest which gets you a spell in the end, or spellbook

Treaties tech might give you a quest that if you succeed, a bad effect could be placed on a random city of the civ with the worst relations with you

Other ideas suggested were army strength, sovereign level, and champion level.

Also- another quest idea would be to have bad effects from goodie huts/quests (quest malus could be solved by doing the quest)

I don't have any creative ideas for these, but I think there would be several good ideas here to flesh out quests some.