I feel Superman books (or at least one of the two) should be his dealing with crazy Earth, Galaxy, Universe, Multiverse threatening problems. Also, he should be seen as special, as the hero all others (yes, even Batman) aspire to be in some small way.
It’s a nice bit of token respect that a character routinely disrespected can use. But the real center of the DCU is Batman in every “real” way. So it’s a bit hollow.