If your germ-bra slips down, it's not going to protect anyone from disease.
As far as I know, the reason most Japanese people carry handkerchiefs is to dry their hands in public restrooms that don't have dryers or paper towels, to wipe their brows in the horridly hot and humid weather, or to clean or wipe down surfaces that they want to sit on or interact with (like a wet bench after rainfall). The one thing they don't do with them is blow their noses or use them to cover their mouths while coughing. When I mentioned this to my husband, he joked that Americans didn't bother with handkerchiefs, to which I said that they didn't have to since they, by and large, didn't spray their bodily fluids omnidirectionally like a bacteria/viral shower when they were sick. We are taught to cover our mouths/noses when we do such things.
So, as you can see, I still don't miss all of the open-mouth coughing that I experienced in Japan and I haven't forgotten how gross it was.