I think there should be a mechanic where you can cancell a quest if you don’t want to follow it anymore, or if you just accidentally clicked it. if you cancelled a quest it would be able to be accepted again if you haven’t completed it yet.
I don’t quite get how this is different from how cancelling quests currently works in the game, this even sounds like exactly the same. Just press L (or J ?) to bring up the quest menu, and you can hide them from HUD or abandon them, in which case they will appear in the radio again. I think that’s what you said.