Bras were actually designed to be pockets for women. We all need to carry small things sometimes so bras were invented to work with the female form, just as pockets were made for men.
Men needed a place to put their wallet, and a way to cover the fact that they were constantly scratching themselves (where scratching = touching their penis). Ladies needed somewhere to tuck their hanky, and a way to show off cleavage so men would “scratch” themselves and want to take out their wallets.
[I totally made this up but I thought it was a genius idea. Just imagine, hundreds of years ago someone knew that someday I would need a place to tuck my music player while I dance with joy in my new kitchen!]