I think when people say "grounded" they mean Steve and Etta; rogues like Dr. Psycho, Giganta, Veronica Cale, and a smattering of hokey Golden Age villains; and (optionally) the vaguely military/metahuman affairs stuff. Honestly I find that those arcs often wind up being dull and forgettable, plus in the hands of a writer who doesn't get the character Diana gets reduced to "strong, very serious lady who doesn't use contractions when she speaks" (which is only mildly preferable to "angry lady who kills things with sword"). Some writers like Rucka and Simone do the "grounded" side of things really well but IMO even they tend to be most successful when they toe the line between the two, e.g. the Medusa arc or The Circle.
I actually loved Azzarello's scale and approach to myth, not to mention Cliff Chiang's gorgeous artwork and super creative take on the gods. It's just a shame that he had no interest in/understanding of the character and instead wrote a gender-swapped Hercules story that got canonized as Wonder Woman and the Amazons. It also led to a long stretch of clueless writers trying to do the huge-scale myth stuff but failing miserably, continually doing damage to the character and her mythos in the process (see: Poochie...sorry, Jason). With all of that considered, it's not surprising that a lot of fans are really gunning for the less grandiose side of things.
Hopefully Historia restores people's good will about the high fantasy, gods and monsters stuff because that's definitely what I prefer. And if we must focus on the non-mythic side...pleeeease give us more Trung Le Nguyen WW. His story about museum curator Diana and Badra in Black and Gold was amazing and I would love to see him do a full GN.