I've never understood the 'we must use minis now!' and the 'It's a board game now!'-type arguements ad debates and flames.
To me, 2E and 1E were much more grid-oriented and wargame/ board-game-oriented that 3E is. 3E is just the first version that tried to make things simpler by using a grid-reference. Every single module that I've ever seen for D&D has been laid out in a grid, often creating buildings and castles in utterly unrealistic forms for the sake of the grid (save for the always excellent UK modules, Ravenloft, Dragonlance and a few other spotty exceptions such as Ravager of Time). All unit references were in 'inches' rather than feet, yards, whatever; obviously a holdover from the wargaming roots of Chainmail. I played 1E for a decade or more and we always used minis. Everyone else I ever gamed with used minis until the things got so expensive that no-one but the hard-core wargamers and later the Blood Bowl/Warhammer people could afford them. After that, we used old minis, or counters or standups or just dice.
I played years of Call of Cthulhu with no map, no minis, etc, and we also did Vampire and other Storyteller games that way. At the place I play the most, space was at an absolute premium for many, many years so we seldom ever used a board or minis there save for times when it was absolutely necessary to know where someone was in relationship with others.
It's certainly possible to play 3E without minis; we've done it since 3E's been out, and we've done it with a grid and counters. The map will usually come out at some point, though, for the same reason it always has: so we know where everyone is in relationship to everyone else in case there is an arguement about cover, ranges, areas of effect, or whatever.
Spells had ranges and areas of effect before 3E, remember? People still have movement rates, arrows still had ranges, and creatures could only move so far in a round. It was just as important to know positioning then as it was now. Any difference now is just an illusion of perception.