I have read that carrying the bow that way is very uncomfortable and may damage the string. Also, something I am trying to find out: how long is the bow kept strung? It seems to be common consensus that it warps the bow eventually, so for storage the bow is certainly kept unstrung. But what about during travelling, or sleeping? It only takes a couple of minutes to string a bow so it would make sense to remove the string whenever you do not expect to use it.

Mongolian's used rather normal recurve short bows, so I believe it was only the Japanese. Chinese bows were also pretty normal, as far as I remember.

Also- I have just read that in 1850s percussian caps for guns have just been invented. So it's not just flintlocks anymore, although it probably would still be common. And bows would already have been in decline for a long time. I would imagine the poor to still use them extensively for hunting? Maintaining a gun would probably be too expensive.