Not everything needs to lead to a public debate. Some things that are inherently oppressive or dangerous must be banned without debate. Some elements of society may complain, but it is in the best interests of society as a whole.
For example, many libertarians propose that all drugs should be legal. This does not mean that the government should not legislate until the public debate is concluded and one vein of thinking emerges victorious. It should ban dangerous drugs in the interest of public safety until public pressure to do otherwise becomes too loud to ignore.
The same applies to the burka. If we accept that the burka promotes gender inequality, the government should take action and ban it in society's best interests. If the public sentiment changes at a later date and the burka is viewed differently, the ban can be lifted. However, in the meantime, it is in the public's interest to ban it.