Only a few (fanatic) fellowships are even able to do ALL paths of all 3 Stages.
Also, Fellowship Adventures are supposed to be fun (I think
), but they often feel more like a chore to a lot of players. Forcing us to do all paths in order to get any rewards (which aren't that great to begin with) will only exacerbate that feeling and result in even less participation.
So, no, I oppose this suggestion.
An inventory list where we can see what badges everything have would be very useful, but I doubt the Elvenar devs are gonna code it in. Still, I do support idea.