It has to do with the fact that you are still expected to show up at work when you have a cold or other similar "minor" illnesses. It's the same in Korea and other Asian countries.
That's not entirely accurate. It's because of H5N1 outbreak 10 years back that people have become a lot more conscious about airborne diseases. It is polite to wear a mask when you are sick so that you don't spread it to other people when you cough or sneeze.
The practice of wearing a surgical mask in asian countries is far more than 10 years old. I saw it in Hong Kong and Shanghai in the 70's.
Not sure, but it definitely blew up after 2003.
Having lived in Japan for around 10 years, in my experience, the vast majority of mask wearers are doing so because of allergies (particularly Sugi). It's pretty rough for a lot of people - particularly in the early spring months. Also why air purifiers are big business here.
I feel like this could be solved with a decent VPN + an occasional webcam.