There should be trading, now for everyone saying no hear me out.
Bungie should have xur come maybe once a month, thus limiting the amount of exotics that flood the game. It would also balance out crucible, and eliminate a lot of complaints. Now you may ask, what shall we do with our strange coins we would have collected by the time he comes back. I'll get to that next.
We should have an auction house, which you could pay for items with strange coins. Here in the auction house you could sell any gear of legendary quality or better. You could also sell upgrade materials, which would create a new use for strange coins. In return slightly creating an economy.
We should also at the end of a raid/strike have 5 minutes to trade anyone that was on our fireteam. We all get duplicates of items we just don't need. Last week I got 4 Hawkmoons in a matter of 2 days. 2 of them were of no use so in the end I got energies.
This is something that all other "MMO"s have and you guys consider yourself one. There is no point in not having a proper trade system.
-
In a word, no.