In his most recent post Berlatsky tackles what I think is a more obvious reason for Wonder Woman's diminished status - Superman. Neither he nor Wonder Woman were originally designed to interact with each other, but are forced to do so within that piecemeal corporate entity called the shared universe. Both characters are meant to represent the highest form of heroism, but when made to coexist in the same fictional plane, one ends up playing second fiddle to the other:
"WW is different than Superman in a lot of ways. But she's the same in that her point is really to be a paragon; the quintessence of heroism...So when you put her in a story with Superman...well, one of them has to lose focus. If it was Marston, of course, that one would be Superman, and it would be all about how men, even superman, have to submit to women, and love their submission, and so forth. But, alas, Marston's dead, and what we get instead is the much more conventional idea that women (even wonder women) are mostly there to serve as supportive figures in male psychodrama."
Which brings me to the other character to be constrained under a similar arrangement. The one that, when he was being published by another company, actually gave Superman a run for his money:
Seeing them stand side by side makes visible the DC habit of collecting characters who are basically embodiments of generic heroism. Wonder Woman's gender at least gives her some level of visual contrast. While hardly the most dignified role, making her a glorified personal assistant, close ally, best friend, potential love interest etc. to Superman at least guarantees her some visibility during the annual super-hero pile-up. DC can also pay lip service to her as the world's greatest female super-hero even when she's not allowed to be the world's greatest hero. That's a lot of BS of course.
Captain Marvel is an idea that seems to have walked out of a child's daydream of what a cool adult should be like. It's not the specific powers that matter because he is power. He's The World's Mightiest Mortal: He's a marvel. He's a superman. That may have been true when he was part of Fawcett's line-up, but what happens when after a long period out of the limelight he moves to DC and meets his rival male counterpart? How do you settle which superman should be the greatest?
You can make them fight for dominance like typical males:
But the outcomes of many of these battles were never in doubt because they're never allowed to unseat Superman's place in the DC Universe. Forget that Wonder Woman and Captain Marvel are beings who should be able to exploit Superman's supposed weakness to magic, or any other hair splitting arguments that fans can come up with. What matters is that Superman has been locked into his primary role as the quintessential super-hero. DC initially shunted off the Fawcett characters to their own parallel universe. But even after they were merged into DC's main universe, Captain Marvel has remained a consistent second or third stringer. If anything, separating him from familiar settings and supporting characters has made him more of an orphan within DC. Meanwhile Superman benefits from a universe which treats him as an integral member: He gets to tussle with evil New God Darkseid on a semi-regular basis. He gets outwitted by Batman at every opportunity. He fights alongside Wonder Woman in DC's version of Ragnarok. And it's Superman and Wonder Woman who have Earth-shattering sex while Marvel barely registers as a presence before getting clobbered by Braniac in Dark Knight II. This is not a question of whether this is fair. This is fiction after all, and DC has assigned Marvel a smaller role.
What's unfortunate is that just as with Wonder Woman, Captain Marvel's original qualities tend to get diluted within DC's environment. The essence of his appeal is the idea that an average child could be wholly trusted with the use of godlike power. He was conceived in an era when super-powers were still treated more as a wondrous gift than as an unsought for responsibility. From the Whiz Comics pages that I've read, he possessed a certain goofball charm that hardly anyone today cares to replicate. But I don't think anyone at DC has believed in that premise for a long time. On the contrary, Marvel's perceived immaturity and naivete are sometimes treated as a dangerous liability, and used against him in Post-Crisis stories like Legends and Kingdom Come.
Superman's seniority also leads him to assume a paternal role towards Captain Marvel's Billy Batson identity. In the recent Superman/Shazam!: First Thunder, the still neophyte Billy at first revels in the use of his newly received powers. But when this leads to tragedy, he loses all self-control, forcing Superman's intervention. While the inevitable confrontation between Marvel and Superman doesn't devolve into the usual slugfest, Clark Kent becomes Billy's mentor because the kid obviously needs moral guidance and adult supervision.
It doesn't come as a surprise to me that the recent Shazam! The Monster Society of Evil by Jeff Smith works very well as a "back to basics" approach, partly because of the noticeable absence of DC Universe elements. But speaking us someone who would on some level find it emotionally satisfying to see The Big Red Cheese upstage the Man of Steel, to most fans the character may simply have grown too old-fashioned, stale, familiar, and that his best days are already far behind him.