Suggestion: Random Encounters

[LilRedAlchemist]

So it's S rank hunts with no fixed respawn timer.
And what you're talking about with class quests/story quests IS in the game already. They're called Guildhests. We just don't get any after lvl 40.

I think OP means more like Pokemon where you walk through tall grass and something randomly attacks you.

Or in older FF when you traveled from one place to another you'd get attacked.