I don't think its the Burka that is the real issue I think it is the hiding of the face from identification. I'm told it's not a religious requirement so that should make it easier to resolve.
Many places have banned the total covering the face in normal circumstances, no hoodies over the face, no masks or ski masks. We have a case before the courts right now, a Citizenship court refused to allow a woman take part in the ceremony until she removed her face covering, both sides claimed the other side was not respecting their culture! I can guess who will win that one!
Facial identification is a big part of todays security, drivers licences, security I.D. Airline travel etc. until the other forms of identification become practical e.g. retina, and fingerprint I think facial I.D. is a must, it can be done discreetly. Q. Do the woman covering their faces still have to go through the body x-ray scan at airports?
It wasn't long ago the issue was turbans.