I played both official and private (pirate) servers, and from all I have experienced, Firestorm offered the best private server experience. It's actually very smooth on the newest expansions, although some of them (like Mists of Pandaria) sure need some love.
I share your concerns about dungeon finder etc., and I believe it could be fun to have some kind of private server with newest content, but also some features removed specifically to make people experience more real human connection, like in the Classic era. I wasn't there back then in the 00's, but even just World of Warcraft Classic and WoW Classic TBC definitely made me experience the game differently. There's just...no rush, and more human element. I like it.
Questing element is still there, and it can be fun, but something about game's pace makes you skip it over rather quickly. Many folks just try to level up real quick and go through dungeons to see the numbers go up - but it's not that every player has to do so.
But, on the other end, the game just became more of everything, and a lot that has changed about it has rather changed about the player base. Nothing stops you from walking out to the Elwynn Forest with your friends and go to the Deadmines, like you always did. On the other end, nothing stops you from racing dragons, either. The content is still there, the core mechanics unaltered, and with the right people wishing exactly the same kind of playthrough you can get all of the old joys yet again.
Maybe more people started playing the game a certain (arguably killjoy) way. But you don't have to, and the game as you know it is still there, waiting.
On the other hand, maybe it will prop up PeerTube for once...