I don't understand the logic of people that propose these types of legislations.
Imagine that your credit card is stolen, and there's a video of the robber using it, but she's wearing a burka, so the police investigation meet a dead-end. If clothes covering the face were banned, the outcome would be different.
The German law already forbid face coverings in public meetings (the law was created to fight a wave of hooliganism in the 80s). Since the law is the same for everyone and supercede religious concerns, banning burkas should be a non-issue.
What do they think is going to happen? These women are going to abandon their faith of their own volition and face no repercussions from their family or community?
Or are they going to just not go outside anymore?
So nothing should be done? Some women wear it be choice, but others wear it because they're pressured by their families and community. The nation has a duty to help them.
When you have something unfairly imposed to some people, the most ethical way to deal with it is to forbid it to everyone, as much as possible. And mentalities will change over time.
This is the logic some countries applied to smoking in public places. To protect those suffering from passive smoking, smoking in public was forbidden, the smokers grumbled that their liberty was infringed upon, and it is still a net positive on the long term.
Some women will be forbidden to go out if the burka is banned. But it won't be all of them, and of those who are, a lot will leave their intolerant family, or call the cops, and as long as the state is firm about enforcing rights and issuing prison sentences, the religious extremism will decrease over time. It won't be without pain, or even a few tragedies, but the long-term effects of having a religion challenge the secular power of a nation is worse.
This remind me of Reddit and what's happening with the T_D subreddit. The mods tried to keep their eyes closed and tolerate intolerant fanatics, hoping the problem would go away if they avoided hurting thier sensibilities. But, as reality proved, the problem didn't go away, it grew and grew until getting out of control. That's the thing about fanatism, it is never satisfied...