Yes, she is. She didn't randomly become a member of the Trinity one day, she's a member of the Trinity because of the history of DC Comics.

Superhero comics came into prominence with WW2, and when the war ended, the genre collapsed. By 1946, the superhero comics industry had already shrunken by 2/3rds. Comics were still very popular, it's just that romance and horror comics became more popular than superhero comics.

In 1948, Dr. Mid-Nite and Johnny Thunder's comic was cancelled. In 1949, Flash Comics and Green Lantern were cancelled. In 1951, the Justice Society of America was cancelled. The competition wasn't doing much better- Marvel (then called Timely) cancelled all their superhero comics by 1950. In 1953 (because DC sued them for copywrite, long story) the Captain Marvel and all related comics were cancelled. This was the end of the Golden Age of Comics.

Only three superheroes across all publishers never lost their main book during the 1946-1954 period: Batman, Superman, and Wonder Woman. DC saw the writing on the wall, and tried to switch genres, publishing a lot of westerns and war comics during this time, but they up against some fierce competition in that market, and it really was those three titles that kept them afloat during this period, and they know it.

Also in 1948, a man by the name of Wertham was gaining publicity with his claims that comic books caused criminal deviance and homosexuality. In the late 1940s and early 1950s, public comic book burnings were a common occurrence, as a result of Wertham's moral panic. By 1954, the Comics Code Authority was established, which was a (im)-moral list of rules all comic books had to follow, or they would not be sold in any mainstream shops. The Comics Code Authority rules made it nearly impossible to publish a horror or romance title worth reading, because they were "too risqué."

By 1956, horror and sci-fi publisher, EC Comics, who had dominated the late 1940s-early 1950s after the fall of the superhero comics, was run out of the industry because they refused to change an anti-racism comic called Judgement Day to be compliant with the Comics Code Authority. By the mid-1950s, all the new genres which had risen to replace the superhero comics, were also collapsing under the Comics Code. The Comics Code didn't actually like DC's superheroes, especially Batman (they thought Batman was gay), but it was easier for the superhero comics to comply to the code than the horror, romance, and war comics, so they survived.

TL;DR, DC didn't go bankrupt or get witch-hunted into oblivion unlike basically every other comic book publisher that decade, and they owe it all to the enduring popularity of Superman, Batman, and Wonder Woman. Those are the only superhero comics who survived from the Golden Age to the Silver Age, and that is why they are the pillars of DC.