Well, you could construct a sort of semi-adversarial game, where half the group control a PC party, and the other half control the monsters. Might even work really well for dungeon crawls, where one DM then doesn't have to handle everything.
I don't see it working quite so well for an ongoing campaign, although it might do. Adding a "random plot complication" deck might well get closer to the ideal.
However, I'm not sure that that's really DMless D&D. All it's done is shifted the rules-adjudication role to everyone (which is a good thing IMO), and shared the storytelling role between multiple people (which tends to be a bad idea, IMO).
It could work, and I would be interested to see it. However, it doesn't sound like a game I would like to play, and if that ever became the way to play, I think that would be the end of my involvement in the hobby.
The reason I would almost certainly would not like that form of game is that I much prefer to DM. It's what I enjoy, and it's something I've gone to a lot of effort to become good at. Remove that, and most of the point of playing has been removed (for me, anyway).