Trading boxes and keys would be interesting, but there might be an issue with the ability to effective sell content though, which is potentially concerning -- bot accounts playing for keys to "sell" or trade to/from people's main accounts. But I think you could design around that and it would end up just fine. :)
Trading skin shards and champ shards seems like something Riot won't do though. The randomization of the system encourages people to actually still buy content if they want something specific, but putting in a trading system would effectively eliminate that and let anyone with resources stored up get any content they want at no actual cost. As a business, that sounds like something Riot would want to avoid.