Would things be any different if women designed women's underwear?

Good questions, although I feel they're entirely beside the point.  It's not about the actual underwear (or burkas), it's about what the articles of clothing represent.  

As I said in more detail above to TBG, the clothing itself is merely a symbol (and often a tool) of the cultural problem, so when clothes are used to manipulate us, ether by politicians or industry, we take it personally for reasons we often can't, or don't want to, articulate.

Maybe we can eventually make language a complete impediment to understanding. -Hobbes