It wouldn't really have made any more or less sense for Maria to have an American accent as it does for her to have a British accent. Nor would it have made any sense for her to have an Austrian accent, as she is supposed to be speaking her own language. It's interesting that, once Julie Andrews and the Canadian Christopher Plummer were cast in THE SOUND OF MUSIC, it was decided that the children and the rest of the cast would be coached to have mid-Atlantic accents that veer towards British, just for consistency's sake. It would have been really incongruous if some of the actors had flat American accents, others had British accents, others had Austrian or German accents, and so on.
On the other hand, as many people have noted, it IS quite incongruous that Julie Andrews retains her full-on British accent in THOROUGHLY MODERN MILLIE, even though there's no reference to the character being British and it's actually implied that she's from a small town somewhere in America.