One may think that the AH may suffer a reduction of competitivity, leading to higher prices, but in an healthy server the gold farmer's farm will be taken over by actual players. Giving the chance to a more fair gameplay where you can go out and farm the materials that you need, instead to see them always farmed by gold sellers that sell them to you, without letting you many room to make gold in a fair way.
Mounts also take up space in your bags, bags which will of course be much smaller. Every bag space counts. With no guild banks, and much smaller storage space, your bank alts are going to be essential. You’ll need to remember to always post everything back to a bank alt, and to remember to get everything from the mail box to the Auction House. Which is only in Ironforge or Orgrimmar.
That's not to say that everyone has an unrealistic vision of what vanilla WoW was like. There were already plenty of people on the WoW Classic forums pointing out that perceived bugs are just recreations of the original game. And as noted before, a flaw to one player is a key component of the original positive experience to another. WoW Classic will surely please plenty of purists in spades. But this goes to show that it won't be for everyone who has fond memories of the game circa 2006.