I'll try to be as short as possible.
Diablo is an efficiency game. Vanilla AH was a plague - loot was scarce, random as hell and most stuff was useless. AH was the only sensible way to get geared for Act4 Inferno until you liked to be walled into act1 or 2 to farm for a self found character.
D2 trading worked because you could do everything in game even as self found (while you were slower) while in D3 if you didn't had gear, you were effectively locked out of the "endgame".
After AH ditching and loot 2.0 we have reached an opposite situation in D3, where farming gear is even too easy for my standards. In current environment, AH is next to useless since gear is not an issue at all. AH would require a more balanced drop/farm situation to be effective.
But then the biggest problem arises: which one will be the most efficient way to get gear? If it's AH, people would just farm gold/resources to buy gear and not hunt for items, which should be the game core (one of the reasons AH was scrapped); if it's farming normally, AH won't have a purpose.
The whole problem is how the game is structured - AH has simply no place in D3. Also, between a missed feature and third party sites selling stuff, i'd go for the first option personally.
I have absolutely zero interest in trading in a game like D3. But it's my point of view and i understand why people would like it back.