There was a time when I tended to disregard the first version of Wonder Girl in favor of the altered version who became a member of DC's TEEN TITANS title. More recently, though, I've decided that the original character definitely occupies a distinct place in the history of femmes formidables.
In essence one could argue that her template was borrowed from that of Superboy: if you have a young audience that's willing to buy adventures of an adult hero/heroine, maybe the same audience will also buy a teen version of same, closer in age to said audience. Unlike DC's Superboy, the teen version of Wonder Woman never sustained her own feature: her stories always appeared in issues of WONDER WOMAN. Sometimes "Wonder Girl" stories shared space in the magazine with "Wonder Woman" stories. Sometimes stories of Wonder Girl, living on Paradise Isle at a time when she had yet to embark on her crimefighting mission, took over the whole book. Eventually editor/writer Robert Kanigher must have decided that Wonder Girl stories might have more currency if she could appear in man's world at the same time that Wonder Woman existed. Therefore the scientists of Paradise Isle came up with a magical machine that allowed the teenaged heroine to occupy the same time as her adult version-- not to mention a "toddler" version, "Wonder Tot," about whom the less said, the better.
I've sometimes wondered why Kanigher chose to emphasize the Wonder Girl version of the main heroine for so many years, giving up only near the end of his tenure on the title. Kanigher had edited the WONDER WOMAN title since 1946 and became its exclusive writer in the following year. In 1958 the original artist H.G. Peter left the book-- whether at someone's behest or not, I do not know-- and the title's most regularly-employed artists were the penciller-inker team of Ross Andru and Mike Espositio. In issue #98 Kanigher and the new artists broke all ties with the Marston-Peter version of the character and formulated a new origin in which the Amazons were the wives of warriors killed in battle and Princess Diana was born naturally of man and woman, receiving her great powers via the blessings of the gods, much after the fashion of the Sleeping Beauty folktale. Eight issues later, Kanigher introduced Wonder Girl, and kept her on a regularly appearing alternative to the titular heroine.
It's likely that the sales of WONDER WOMAN had slipped during that period, prompting the creators to try different strategies to pump up sales. At the same time, for professional comics-creators the important thing was to produce material efficiently, to meet the ever-steady demand of commercial comic books. Interestingly, during the 1950s Kanigher was less known for his work with superheroes than with war comics:
Starting in 1952, Kanigher began editing and writing the "big five" DC Comics' war titles: G.I. Combat, Our Army at War, Our Fighting Forces, All-American Men of War, and Star Spangled War Stories. His creation of Sgt. Rock with Joe Kubert is considered one of his most memorable contributions to the medium-- Wiki page on Robert Kanigher.
A lot of Kanigher's Wonder Girl stories resemble the stock war-stories motif of the "green recruit;" the guy who doesn't yet know how to conduct himself in combat situations but who over time develops the requisite skills. Thus Wonder Girl allowed Kanigher to re-use favorite tropes from his war books, to maximize his productivity.
In terms of quality the WONDER GIRL stories are largely of a piece with those of WONDER WOMAN: the daffy, make-it-up-as-you-go-along aspects of the stories is moderately entertaining, but rarely compelling. Kanigher never pushed himself on this title, with the result that every story reads pretty much like every other one. Wonder Girl's tales were usually a bit less overtly violent than Wonder Woman's, so Wonder Girl's feats were usually less about defeating villains and more about outmaneuvering beasts and monsters, like her duel with the shark in the Irwin Hasen cover above. On the plus side, though, she and Supergirl were the only two teen superheroines that female readers of the period might have enjoyed, though on the whole Supergirl's adventures were better written. So Wonder Girl does hold a definite niche in "formidable history," though it's a place largely superseded by the independent version of the character developed in the TEEN TITANS continuity.