I've known female Alexes, Chrises, plenty of Charlies, even a
Stevie (
Stephanie). NNs don't always actually have any gender significance. Most of the ones you mentioned are just abbreviations. No reason why
Charlie should be less valid a nn for
Charlotte than
Lottie or
Alex less 'female' than
Sandra.
I don't think it's got anything to do with downplaying or concealing the fact of being a woman, just personal preference. Well, nine times out of ten, anyway.
:)