Well, "Batboy" rolls off the tongue a little easier than "Batman," too. (And nothing is as awkward as "Captain America.") It's a respect issue.
And frankly, "Power Girl" doesn't flow all that well either, which is why everybody calls her Peegee or Peej. Pee-Dub would be a completely lateral step.
If it's really an issue, though, we could graduate her to "Superpower" or "Powerhouse" or something instead.