Maybe calling it "Superflat" is misleading, since Murakami and his ilk really own that term. But I feel that Anno and Murakami are coming from the same place with this. Both have to do with the perversion, flattening, or abandonment of any kind of transcendent depth or meaning in their work. Like the 60's pop artists before them, EVA is kind of like a parody in the way it takes this rich Biblical lore and symbolism and "deifies" it as a kind of paper-thin, transient, pulp pop-culture. If there's any depth, it's to be found in the shallowness itself, or a kind of weird commentary on the nature of otaku culture or art in general. It's all in the surface technique and aesthetics, much like some excellent Floating World Ukiyo-e art. I think Murakami sees Superflat as a kind of postmodern Disney version of that Floating World sensibility. And when you consider Anno's other work it makes sense to put him in the same camp.
I think if you're desperately trying to extract anything BUT face value from EVA, you're kidding yourself. Because in this case, everything IS the face value, and it's not any weaker because of it.