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.
Note: My goal here was to create a comprehensive list of everything you'd need in order to learn to play any class (from Level 1 to Naxxramas)—meaning I am only including class-specific resources here (so no profession guides, general leveling guides, etc). Teeb's Resource list is much broader in scope, and I highly recommend you take advantage of it (as it contains a plethora of non-class specific resources as well). If you're not aware, Teeb is also responsible for the Race & Class Comparison Tool, Dungeon Tier Sets Gallery, and a huge variety of other insanely useful resources.
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.