No, no, no. Very bad idea for Destiny if trading becomes 'freely' allowed. As frustrated as you might be by the RNG loot system, surely the idea of being handed what you want will ruin the fun in wanting it? Where's the fun in continuing to play? Be honest, when got the Gjallahorn, Vex, Suros, Fatebringer etc. how did you feel? You felt happy but then you felt somehow empty didn't you? You asked yourself 'what next' didn't you? Trading will kill the addictive nature of the game which is why most people play it in the first place.
Now, having said that, trading with the other 2 members of your fireteam following a strike/nightfall etc. COULD work but needs careful thought.
What do Guardians think?