My only thing on this would be having yet another currency to try and keep up with. And, depending on the rewards, I imagine it'd have a 'weekly cap' as well to keep it from being 'wait til easiest EX and then spam farm for rewards' (altho that may also still happen).
Other than that, I think it'd be interesting. I didn't do a lot of EX primals after Ravana and Bismark, so having an incentive to go back and do others would be interesting and one way to do these old contents without wasting hours in the PF. WT has helped some but, as you said, you can do it unsynched so there's no helping those at level and first timers unless they happen to find a WT PF (which I don't see anymore on Crystal nowadays). I don't think it'd hurt anything, although the queue might be pretty long depending on the primal.
Now, one thing you can do to sweeten the deal is, like say Sephirot EX is up on the DF. If you complete it you are guaranteed 1 of his saps, or something of that nature. You can make it 2 for "Adventurer in need" if you want. Will that mess with the market of said items? Sure, as much as the old reuse 'abuse' did. At the same time, it might also revitalize the market of that particular item. Honestly I think it'd be a cool implementation.