I really don't see why bras are a modesty issue at all. The top worn over the bra is what determines whether a woman is modest or not. Bras can be designed to present a woman's chest in the most noticeable manner, it could be more modest to dispense with them. Depending on the nature of the boobs in question of course, the opposite can be the case obviously.
I'm glad you mentioned this, because two different avenues have developed (no pun) on the bra issue: Modesty and Health. The modesty factor really is primarily controlled by the overlay (clothes) rather than the support frame (bra); the bra acting as more of a "modifier". I believe the OP was more interested in the Health aspects of bra v bra-less.
As with any issues, there are steadfast, overbearing, proclaimers of polar opposites on the issue. The ones who say that they should be wrapped up all the time and those who say that they should be free all the time. Again, as usual, the truth is in the middle and often supported by facts which people are innocently ignorant of or actively ignore in order to support a tangent political agenda.
In this case, common sense really does match science. If the breasts are left to hang for all of time, they WILL sag; however, to my knowledge, and i have not read any research saying otherwise, there are no health risks or modifiers in doing so. It is the natural order, the baseline. If the breasts are bound all the time (even correctly fitting ones) there IS a SLIGHT increase in health risks and there will still be some sagging later in life, but just not to the same degree. As it is, "Aesthetics", shall we say, is more of an issue with genetics and muscle tone anyway. The big problem, is with the 80% of women who wear the wrong sized bras which DOES greatly MULTIPLY the originally slight risks in wearing one and this is the data used by the 100% bra-less camp as their argument.
If I can go full-guy here for a second (as if i hadn't already) it's kind of like riding a motorcycle versus driving a car. The natural order is to drive a car. No greater risks involved other than the normal baseline risks of driving a car at all. If i choose to ride a motorcycle, I ride the right bike with the right gear. Risks are increased slightly, but I have the benefit of going places quickly and with much more enjoyment. If i ride the wrong bike (too heavy, too big, too small, not enough power, too much power) with the wrong gear (no jacket, wrong size helmet, no face protection, sneakers), risks are
multiplied with no increased benefit and may hinder my overall enjoyment.
Ok, i'm done.