To me, the problem with "Batwoman," "Batgirl," "Huntress," "good Catwoman" etc., is less that they take away from the "urban myth" aspect and more that it is just too "Supermanish."
I wouldn't mind it so much if the "Bat females" were treated as, for lack of better term, 'fans' who are inspired by Batman and try to imitate him (sometimes with a fair amount of success), but are generally considered by him to 'posers.' However, even when DC tries to portray Batman in that way they always end up making him the big "dad" of some sort of "Batman family."
And, that's not what I want in a Batman portrayal.
