The whole "bra burning" feminist stereotype has its toesies in fact, with some women suggesting bras are only worn to confirm to a beauty ideal and pointing to cultures where sagging boobs are considered normal. Of course some of these cultures also make women stay in a hut while menstruating, thus illustrating that "traditional in subsistence cultures" is not synonymous with wise.
|Ancient Greek breastband|
In fact the centuries old Stethodesme or Fascia (cloth or leather breastbands) were essentially a more inconvenient version of the bra. If western culture had not headed off down the path of corsetry (a.k.a. binding things that don't jiggle) we might actually have developed a decent sports bra by now.
For those not disturbed by their jiggling, that's cool. Personally I prefer to do without it and that is a totally valid choice, thank you very much.