It would just turn the boards into a trade market (regardless of whether it's allowed or not) and people would spam you with requests looking for skins. It would also be abused to transfer content between accounts at risk of ban so they can avoid losing them, and will also result in people getting scammed (either by lying about the value of an item, or stealing everything from a compromised account).
Not only would the results be potentially catastrophic, Riot would lose a lot of money out of it and probably have to remove or revamp Mystery items (it's not a gamble if you can just trade it for what you want). There are obvious good things about it, but the negative side far outweighs it.