The big problem is, that old Azeroth most likely doesn't exist anymore. There was a lot of work done to make the old world flight-compatible in Cataclysm. Old-World Azeroth used as many 2D poster tricks as it could to save on space and loading with the backgrounds. Its why the flight posts always had a bit of a wonky path.
I'm willing to bet that, in order to save space, they overrode and removed whatever they needed of the old world with cheapest wow accounts the newer content. While that might not matter much for some areas, other areas (such as the Barrens for instance)had received drastic overhauls which would have to have the old version of Barrens reinstated alongside it.
That means more storage space. More storage space needed means bigger install and thus potentially more disks for retail copies. That's a lot of bloat to reinstall just for a couple hours of nostalgia. Not to buy world of warcraft accounts to mention the chance of drastic bugs to pop up like the infamous Final Fantasy-11 like weeklong cooldown shamans ended up getting as part of their tier effects.
I think it was a control file. It kept all the differences listed, and displayed the old world. Once this file was deleted, it displayed the "new' world.
Since then, Blizzard has done two "cleanups" which reordered the files, and reduced file size. It probably removed some of the older files. If this is the case, then it would require more than the 10MB that file took up, but it wouldn't be a drastic change.
The funny thing two people with the same client could see people with and without the file. Someone discovered if you deleted this file yourself, you saw the new world. Other people on the PTR, who still selling wow accounts to saw the "old world" still saw you, and count interact with you, but if you were standing or walking on something new, you looked like you were floating in the air to them.
And yes, dungeons are hosted on different servers. They are hosted on the same ones raids and BG's are hosted on.