I can't agree with you when you say "Nobody has to wear a bra". Today's teen "have to wear a bra". Every school dress code I've seen states "appropriate undergarments must be worn"- read bra. Even in schools where there is no official dress code, a girl who goes braless these days is harassed by her school mates and called a slut or 'hoe'.
Why the concern over teens? Because if today's teens are brainwashed into compulsory bra wearing, they will be bra-wearing adults years from now.
I brought up this photo from 26 years ago to contrast it with the teens of today who are embarrassed even if a nipple make a bump in their shirt, and to show what a challenge brafreedom faces today.