I can easily accept a Diana with greater powers than the other Amazons, or prophecies surrounding her birth. A lot of that can vary depending on what types of stories are to be told.
But I think that the relation between Diana and the Amazons is the foundation on which Wonder Woman the social icon rests. With "bad" Amazons around her, she is a token: the exceptional woman. With "good" Amazons, she is an alternative. With "bad" Amazons, Diana becomes a person who isn't here to reform our society, but to reform Themyscira.
Part of that probably comes down to that Marston wanted to, and had to, depict Themyscira as a vibrant and vital community, because none of us comes from there. As Wilson noted in an interview "lots of us are from Kansas, none of us are from Themyscira". Thus Clark Kent's upbringing could easily be done using shorthand forms.
Marston didn't really spend much time on Diana's upbringing either. The real differences were that Diana regularly went back to Themyscira, and that he spent some time embellishing on the Amazon backstory. The same was true of Pérez.