The real threat the burka poses is that it might restrict one's arms when trying to mitigate a fall. There was this one time when a kid tried to use a burka to buy some booze. Didn't work.

I can go either way on whether banning burqas and niqabs is a good idea, but I'm willing to bet that for every woman who thinks "oh no, now I will be exposed to the eyes of the ungodly" there's another who thinks "hurrah! My stupid husband can't make me wear this hideous sack any more".
To say the wearing of such garments is a 'choice' actually begs the question. Self-harming, anorexia and suicide are 'choices' but that doesn't mean we should not intervene when we see them being made.