While I agree that minis are optional in all the editions (even 3E), I think some versions work better with minis and some without. Here's my view:
OD&D: A development of miniatures rules. Very close relationship, both because of terminolgy and because the tactical rules assume the use of Chainmail, by default (although Chainmail is not an absolute requirement). Minis a natural fit, but not absolutely necessary (largely depends on how the referee runs combat, which is not explicitly defined by the rules).
AD&D: A development of OD&D. Adds explicit movement-in-combat and engagement rules that facilitate play without minis (and, if run as written, makes the use of minis for precise tactical positioning difficult). Retains some terminology and artifacts from OD&D and Chainmail. Works exceptionally well without minis. Minis can still be used, in an abstract fashion, or can be used more precisely with some minor house ruling of the RAW.
Classic D&D (B/X, BECM, etc): A separate development of OD&D (parallel with AD&D). Drops some of the mini/wargame-specific terminology and artifacts. Uses yet another system for handling movement-in-combat (10 sec. round instead of 1 min round, different movement rate, etc). Works very well with minis; they're helpful. Works good without minis, too.
3E: Mini use assumed and integrated into the design of the system. Works very well with minis; they're very helpful. Works okay without them, too.