LU:
With all due respect, I think you’ve exemplified the unconvincing arguments used against burquas. What’s wrong with something being “done publicly”? The same could be said about (depending on the community) tights, tichels, or even full-lentgh sleeves. Should all of those also be opposed?
It happens to be true that many of the burqua-wearing women belong to cult-like movements. But that really has nothing to do with whether actually wearing a burqua is good or bad.