It possibly came from the Cambridge University tradition of giving a large wooden spoon to the student who scored lowest on final exams.   No wooden spoons were given after 1909 at Cambridge, when the scores for exams started being read in alphabetical rather than score order.  One theory is that early on in the Six Nations, many of the players were from Cambridge and carried on the wooden spoon tradition after it no longer was a part of university life.
In the six nations, why is 'prize' for the team that does not win a single game called "wooden spoon"?