You know, that doesn't really bug me, because it's Captain Marvel; they're not taking their world-building seriously, but no one's pretending otherwise, that's not the point of the story. It's just about having some simple all-ages superhero fun. 'S like looking for historical accuracy in Dr Quinn, Medicine Woman versus looking for it in Xena.
I do find it annoying when it ends up intersecting with the rest of the DCU too glaringly (trials of Shazam frex), but when that happens the problem isn't with the Shazam mythos itself, it's with the post-Crisis world merge. I just don't think Captain Marvel *works* the way it's supposed to in a shared universe, in a very fundamental way that's unique to it - other characters might be more awkward (there's nothing in Billy's world that's as sticky to reconcile with the rest of the DCU as the insolubility of Oracle's paralysis or the coexistence of the Wonder mythos with the Sandman one), but while Billy fits perfectly well on a myth level, he loses the whole point of him on a thematic and mood one.