I'd say you're overestimating the margin between ED and D&D mechanically.
The real difference is simply that the writing for ED takes time and effort to embed the classes into the world or Barsaive. D&D could absolutely have done the same. It doesn't, but instead it makes a huge number of incredibly specific assumptions about the world, which I've discussed, which generate a hyper-specific implied world (though the exact nature of said implied world varies from edition to edition - 3.XE being the broadest and closest to "generic fantasy", I think, esp. if official-optional rules are in play).
ED didn't get popular enough, but I daresay if it had, we might well have seen it support other settings. I disagree with your claim it supports a narrow range of fantasy, at least if we're talking mechanics. That is an impossible claim to accept when Vancian casting exists, when HP exist (and there's no mechanics to get around them - you just knocked out about 90% of literary fantasy settings right there - I notice Worlds Without Number DOES have a way around HP - execution attacks - which are different to and more appropriate to most fantasy than CdGs), and so on.
I can't say ED supports a wider range of fantasy mechanically, but I can say it is at least as broad.