From what I can tell, the big dog in the fantasy miniature wargaming world is Warhammer. To go head-to-head with Warhammer (and Games Workshop), you'd need an edge. A D&D miniature wargame sounds like it would have that edge. You could use your D&D characters in large battles, you could use many of the minis in your regular game -- we could all use a few dozen Orcs, right? -- there's lots of great synergy there.
So why wasn't Chainmail compatible with D&D?
Certainly there are some technical hurdles. Tracking Hit Points for dozens or hundreds of units would be a nightmare, so you'd probably want to replace Hit Points (at least for "mooks") with a "stateless" system, maybe a Fort Save to avoid dying.
And you wouldn't want to deal with movement, Flanking, and Attacks of Opportunity in minute detail. Maybe units would follow strict rules on movement to keep things (pardon the pun) moving.
Would you need a whole new system with new, incompatible rules though?