If you seek proof, you need only look at most any other similar style game where trading occurs. While it does certainly add a facet to the game that can be desirable, many of those games have implemented artificial controls to limit what can and cannot be traded, such as "Bind on Equip" vs "Bind on Pickup". For all the good it can offer to a game with a robust gear inventory, such as more traditional MMOs, it invites almost as many problems.
In the case of Destiny, the gear inventory is not nearly varied or large enough to even justify such a system, not to mention that there is no means currently to prevent a character who just made level 20 (which can be done in a day or two) from instantly becoming level 28 with a few pieces of traded armor. It's been discussed at length in numerous game design articles that statistically, players who feel entitled to have everything the game has to offer right away quickly become bored and leave the game if there is no sense of achievement behind acquiring said gear or level. In other words, it's not healthy for the game to allow players to get whatever they want.
Furthermore, in-game economies can adversely affect the game experience itself through such practices as selling items/gear for real money, which invariably invites all manner of negative behaviors, such as scamming. This in turn increases the support costs for the game studio when they are required to address player submitted tickets for stolen items, investigating reports of criminal enterprise (e.g. someone selling their intellectual property for financial gain without consent) or player ToS/EULA violations (e.g. scamming), and then being forced to apply appropriate disciplinary measures against the accounts of those players. These are all problems (and costs) that Bungie and the players of this game fortunately do not have to deal with currently.
When you ask yourself what are you actually gaining through an in-game trading system in Destiny, the answer is convenience. It's convenient to trade those Warlock raid boots you got on your Titan for Titan raid boots some Warlock in your clan got. But there are better ways to address that if Bungie makes some smart changes to their RNG system, such as only awarding class specific gear in raids or from engrams. I'm far from alone when I say that I'd rather see them do something like that than implement a trade system that only ends up hurting what is an otherwise great game in need of a few minor changes.
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That would be a good solution too. Fix the RNG to award meaningful stuff. I'm working 55h/week, I still like this game and I still want to play it but I'm not going to start a second class. I just want to get drops for my class only as I can't care less about that exotic armor I got for the warlock which I will never play.