random thought: do flat girls need bras?
Short answer: no they don't. No matter if bras do prevent sagging or not, it's not an issue for A- and B- cup tits. They just have have the sagging problem.
But sadly almost all flat-chested girls do wear bras, not to prevent sagging, but (1) to hide their breast, especially the nipples and (2) to pad and enhance the size of their tits.
I prefer busty girls to flat chest but I could like flat chest girls a whole lot more if they learn to (1) be proud of what they have, (2) be more open minded to exposing their chest in public. I don't mean all A-cup girls should be streaking around topless, but consider not wearing a bra on some days, or wearing very thin fabric bras or wear tight fitting clothings. Depending on situations (e.g. out for dinner or clubbing etc when lighting is dim), lets the guys enjoy a deep-neckline or let the shape of the nipples show thru the shirt or blouse. Instead they tend to put on half an inch of padding and underwire and whatnot to try to make their A/B-cups looks like C-, and then when you undress them it's a disappointment.
Flat chest girls tend to be slimmer and they should use that to their advantage, wearing tight T-shirt with no or minimal bra and maybe sometimes show some tummy or wear a tank. Expose the back to advertise the bralessness, tell the world "there aren't any melons here but all of them are real!" (not padding). I'd be much more interested in a A-cup girl without padding than a C-cup girl wearing a padded bra, because mentally I'm already discounting almost all girls by one and a half cup-size.
Back in the 80s, bralessness was much mroe common. Now I never see un-hidden nipples in public. It's possible (even common) to see short skirts or hot pants or whale tails or massive cleavage, but never see nipples. Even when I finally encounter a women not wearing a bra, it's still guaranteed you would not be able to discern her nipples thanks to padding (stick-on or sewed into her cloth) or lacking all that, scotch-tape. It's much more common to catch a glimpse of a woman's panty (going upstairs or on subways) then to catch discernible nipples under clothing.