You wouldn't have to have all zones running if you wanted to make it a single player version of EQ. 2 zones would suffice, because well...1 player can only be in one zone at once, so the other is there to make it possible to zone into a new zone.
A single player type EQ would be interesting, but it would take away from the overall immersive feel of being in a game with hundreds and thousands of other players.
Lords of Everquest will be a diablo type EQ game that will be single player from what I understand, and will follow along with the same EQ storyline that the online game does. Perhaps you should check that out when it's released if you're into single player type games.