Trading wouldn't break the game. I don't see a difference in people who afk in a game and then come back to shoot a rocket at the last boss and are rewarded with an exotic; versus being in a fireteam and your teammate happens to get their 6th ghorn so you trade for it.
I think trading should be limited to people in the same fireteam that completed said activity. Rarity for rarity. Upon trading, the weapon would lose all xp progress(if you were to have open trading in the tower).
I play with my friend almost every time I get on. There has been times where one of us will get something we either don't want or need, yet can't do anything with it. Then again, Xur has kinda been that person you can go to get your exotics if they don't drop.
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The fireteam trading has been brought up a lot in here so far. I think trading rewards that you get right after an endgame activity could work. Open trading whenever though would not.