Although they're a super cool design, the wishes have never really taken off in cube. You need a pretty specific deck where the flexibility of one card turning into two or three from your sideboard is worth the tempo loss of spending 2-3 mana up front. In addition, do you really want to leave these cards you're wishing for out of your deck in the first place? Generally what you want to be wishing for are narrow but powerful cards for a particular situation, and these kinds of cards tend not to be worth including in a cube list.
Could it be possible therefore to design a "wish binder", separate from the main cube, that you are allowed to wish from? In this case, Burning Wish can run duty as a storm finisher via Tendrils of Agony or Empty the Warrens, a build-around sweeper as Wildfire, or allow completely new archetypes by fetching Doomsday, Ill-Gotten Gains or Worldfire.
I think the design of the binder would have to be pretty limited, with perhaps only 5-6 cards per colour maximum, but it can allow for narrow cards to be included without ending up being 15-pick filler most of the time. If you run Living Wish, perhaps allowing players to wish from the Utility Land Draft as well as the binder could also work.
I would like to try this, but I am coming up a bit short on interesting targets to wish for, particularly as far as creatures go (Doran? Soulflayer? Yavimaya Enchantress?), so any suggestions would be welcome.