Hard to say what Grant Morrison's greatest contribution to super-hero comics is. But if I had to...
Part of what's great about DC's Silver Age comics is their imaginative mythos. Weisinger's Superman Mythos and Julius Schwartz's Justice League of America Mythos are more than just "continuities" (like the serials that made up the Marvel Universe): they are works of art in their own right, creations that have the same kind of inetegrity as P.G. Woodehouse's Jeeves stories or Lewis Carroll's Alice books or the Ellery Queen mysteries. They are finely wrought - intricate - like clockwork. (I'm influenced here by Mike Grost's informative, interesting, and in-depth criticism of these comics.)
Bronze Age comics placed elements of the Silver Age mythos in a dialectical relationship with "real world issues". The Adams/O'Neil Green Lantern/Green Arrow run is my favorite example. IMO, a lot of the power of these Bronze Age comics comes from the contradiction between "realistic" and "super-hero" NOT being resolved. However, for other people, this contradiction is a major problem.
(Bronze Age Marvel is different from Bronze Age DC because of the difference between Silver Age Marvel and Silver Age DC. For one thing, part of Stan Lee's original strategy was to add "real world" elements into his super-hero comics. For another thing, the Lee/Kirby Marvel Universe was a shaggier beast - much more ad hoc - than the Mythoi crafted by Weisinger and Schwartz. So in Marvel's Bronze Age comics, "the real world" isn't opposed to the Marvel Universe: rather, the comics just continue to add more bits of "reality" to the Marvel Universe. These bits are never fully digested, but they aren't set up against the fantastic elements of the comics in the same way. GL/GA is explicitly about the fanastic encountering the real world.)
Much of DC's "Modern Age" of comics represents an attempt to resolve this contradiction. The Crisis on Infinite Earths invokes a science-fiction premise (multiple worlds) in order to do so. John Byrne and Roger Stern's Man of Steel re-boot attempts to update the sci-fi underpinning of the Superman Mythos.
I don't think there's anything wrong with this project, in theory, but in practice it seems to have lead to a cycle of diminishing returns. The "reality" goal posts keep moving putting the Mythos under more and more stress: hence the necessity for more Crisis-like events. The original Weisinger/Schwartz clockwork became the central cog in an unwieldly, patched-together machine, always on the verge of flying apart.
Grant Morrison's great contribution has been to ignore all of this and return to the kind of comics done in the Silver Age. Morrison's comics are New Silver Age comics, cousins of the New Space Opera sci-fi novels.
In Doom Patrol and Seven Soldiers he crafted his own Mythoi; his JLA existed in its own little New Space Opera pocket of the DCU; his All-Star Superman is a New Space Operatic recasting of Weisinger's Superman Mythos.
The point here is that in none of these works does "reality" play any part. Morrison gives them their own internal logic and integrity.
So that's my suggestion: Morrison's greatest contribution to super-hero comics is to save the DCU from collapsing under the weight of those lingering, unresolved Bronze Age contradictions between the Mythos and the real world.