I don't think Diablo's downfall was its AH, but the total lack of "endgame" content. There was nothing to do once you were geared up except run the same content endlessly (and it was literally identical each time-almost nothing changed game to game).*
The AH accelerated the problem and made it painfully obvious to players because everyone got to the end game faster through buying gear. AH or not, the problem was always there, and would have ultimately motivated me to stop playing; it just happened faster.
The lesson for me is that the content you play end game really has to give you a reward beyond gear. Community badges, titles, collectibles, and other rewards keep players playing once they get the set-up they want. I loved the "skull" system in Reach, and the daily challenges were enjoyable scenarios that kept me playing and improving. It also kept me playin for the pleasure of playing and overcoming a challenge. In games with items (like Destiny and Diablo), we still need challenges and rewards that don't revolve exclusively around better items.
*Also, no skill trees were a problem. But that's for another post...
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You are right about the AH accelerating the effect, but if the AH wouldn't have been there in the first place it would have taken longer for players to achieve these goals and thus allowing Blizzard to work on a better end game while players were still finding Inferno challenging enough and the drops rewarding enough to be upgrades. With an auction house, the second you realized that you couldn't get past a certain point of Inferno, you just farmed gold endlessly and bought what you needed on the AH. That is boring as hell.