Well, the burka serves a dual function of protection from the elements and covering up bits that they don't want just anyone to see. We have a similar custom here in America which we call clothing.As far as I know those burkas, durkas or whatever were made in order to cover the woman's body so she wouldn't attract Muslim males.
Care to elaborate as to how this symbolizes choice?
Now some women choose to dress in a fashion that is more revealing than others, often intentionally made to be provocative to men. Now there are many other women who choose to dress much less provocatively because they don't want to look like a slut.
The thing is that dressing like a slut is a relative concept. In America, someone who wears fishnets, ridiculously high heels and a too short miniskirt is generally considered to be dressed like a slut even though all of her bits are covered.
In a nudist colony someone wearing much less would not be considered a slut, so in order to dress like a slut in a nudist colony, a girl would have to paint the words "insert here" on her body with a arrow indicating the point of insertion.
To a woman who perceives her hair as being a very sensual part of her body that she doesn't want men ogling at, she might wear a burka in order to not feel like she is dressed in a slutty fashion.
A law forcing a woman to show off her hair is no more justified than a law forcing women to show off their tits.