“Why can’t we appoint say, Canada and Japan, and tell them that they can handle the continuing drama of Israel and Palestine?”
They would never do it. What interest would Japan have in the matter?
Well, you're right, the Japanese might very well tell us that the best thing to do is to quit funding both sides (the Israelis and the Palestinians) and to let the parties settle their own dispute in the way that they think best. Maybe the Japanese would opine that they can't solve the problem for the Israelis and the Palestinians.
I've just become convinced that we can't solve all of the world's problems and this is one of the problems that experience has shown us that we can't solve.