Considering all of the off-game 3rd-party trading/auctioning/etc. (both for gold and real money) that went on with Diablo 2, why would you say that?
Also consider that, before eBay cracked down on it, items were even being auctioned off on eBay with Diablo 2.
Quite obviously there was significant demand for this sort of thing with Diablo 2 - which is why it was put in with Diablo 3.
The removal of the AH won't eliminate people doing stuff like that, it will just clutter up chat again, and move things back onto 3rd-party websites again.
Is it really more enjoyable to spam chat with "xyz for sale or trade!" or just salvage any item which doesn't have a couple of green stats without even giving it a second thought?
You have to consider the impact it had on the game. It was balanced around the AH existing, and making loot drops have such an insane stat allocation that you'd have an abysmally low chance of finding anything worthwhile for yourself. It isn't fun to grind gold and spend hours on the AH searching through pages of gear to find an upgrade at a reasonable price. The worst part is when you finally come about a significant amount of gold only to spend all day on the AH trying to figure out how to spend it on the most optimal upgrade possible.
It may seem like it makes sense to add an AH to the game because it does make it easier it trade, but the negative impact far outweighs the convenience. Being able to upgrade your gear by playing through the game yourself and with friends is much more enjoyable and true to the genre/series.
I'd also like to add that those websites, regardless of the AH, still existed and were used for D3. Private trading through those means will always exist. I also feel there's more of a sense of community through trading with people personally, rather than through a menu.