Picture this: you and your friends are in this small little AH community. For simplicity it's just and one other friend. You go on and play and gain 1000 paragon and all the gear you ever wished for. Your friend quits just after he hit 70. Your friend comes back. Now he instantly gets flooded with your "gg gear" that you obviously don't need. He has 10 minutes playtime on level 70 and his gear is absolutely finished. All he needs is rift keys and maybe a few hundred paragon (which you as a good friend give him by dragging him through a few GR80 runs).
Result? Your friend has 2 hours played after coming back but nothing to farm for. The entire purpose of the game (gearing up), all the fun parts, are entirely lost. He is wearing (and will be wearing) zero pieces of gear he has found himself. Attachment to the character, to the game? None.
Your friend will be offline tomorrow again, and not come back to Diablo. Ever. But hey, at least you got his money!
Auction house has always been terrible, will always be terrible, and I hope it never comes back. If you're into trading sell your soul and become a broker at the New York Stock Exchange. Well, or play Path of Exile. But in Diablo 3, you won't find your new business opportunity.
Thanks, but I hope this explains why no one wants the AH back (except for the "nice individuals" that made thousands of dollars in D3V - please go away). And from hearing some of the D3 developers' responses to ideas like yours, I think they have similar thoughts. Again: D3 = no trading. PoE = trading. Play a different game, but we have danced with the devil and killed him for good.