Even if we were to accept the premise that most women who wear burkas have them forced upon them (Which you never even tried to prove by the way,) that is a familial concern and is no different than a conservative christian father forcing his daughter to wear her skirts at a certain length. Not only is it not the government's business, but given the egalitarian empowerment that a western education and western opportunity brings to immigrant women, there's no reason to say that I am unfair in saying that the expectation is on the girl to move out and make her own way in the world, away from her husband or father should she find their demands untenable. This isn't Saudi Arabia where she can't leave home because where else would she go. Women's shelters, Various help hotlines, comprehensive social welfare, as well as an omnipresent culture of sexual equality where people are expected to respect one another and treat each other fairly all work in their favor.
So it all sounds to me like your problem is one of domestic 'abuse' which isn't solved just by banning a damned hat. Not that it matters since this is all just a pretext for taking someone's rights away.
Of course banning a hat won't solve the entire problem, but if it has a chance of helping even a little bit or
sending a message as to what is acceptable in a civilized society, then it might be worth trying. Along with a lot of other small things that nudge the society into the right direction. What am saying here is to keep some common sense perspective when tossing around hyperbole like "taking someone's rights away".
War, overpopulation, climate change = Huge global problems.
Crime, inequality, poverty = Big problems in some parts of the world.
Mysogynistic religions oppressing women = Significant problems for some sub-cultures and countries.
Banning a hat = A "problem" so fucking irrelevant that I don't see why I'm even bothering to argue about it.