this is hilarious and also a great idea. i dont see any reason why you can't play a few million games against itself and other engines and see where it takes you. less efficient than alpha zero probably, but how much so?
The same algorithm could be applied here.
Still, I think that there's a chance it could work well. Each move could be prefixed with the final outcome of the game, which is the technique either alphazero or muzero uses.