That's very generous of you - "shortsighted" is not the word I'd have chosen. Dune seems to spend his life worrying about these things, poor thing.
The burqa isn't an obligation for muslim women, it's a cultural aspect and modesty can be maintained in other ways. As for showing herself to the police officer: well, Muslims are known as one of the people of The Book. In the New Testament it says "render unto Caesar that which is Caesar's and unto God that which is God's" - so the obligation to the law comes first.