Barry might have better reasons.
I view Burka (the complete one, with all its variants) as more of a traditional attire, than a religious one. Yes, I have studied Soorah Al Noor, Al Ahzaab, Al Nisaa and Al Hujuraat. I also have consulted the most authentic texts of Hadees e Rasool (PBUH) on the subject.
To me, wearing a religion sends across powerful messages all around. Responsibility of someone wearing a religion increases manifold, whereby they are considered to “represent” the religion to common eyes. But then, common eyes don’t only see. They read, observe, feel, interpret, analyse, co-relate, deduce, and make opinions too. They read actions, most of all. And to me, the burka gives a message that ‘I choose to be invisible, though I can see everything and everyone’..