Ok, you are obviously right. They have intentionally and specifically stacked candy canes heavier than the other collectibles. The evidence of the trading activity is sure proof, since it's a clear result it must prove a clear cause, there can be no other (those people who don't trade because of what they have collected what they want are irrelevant).
Why they would possibly do that when it makes no cash-flow difference to them is a great mystery but I suspect a malicious programmer that decided to alter the random routines in that way because they either love candy canes or hate the other ones. I too have more canes than other ones. And I don't even like candy - so I think I'll take it personally too.
Three choices I guess: Stop collecting any of them because obviously no matter what you will primarily get canes, trade the best you can, or take what you get and make the best of it.