Why are Chinese stones half-convex?
From the manufacturing standpoint, a few thousand years ago it was easier to produce stones that were convex on both sides. Before the Tang dynasty, because of this, all the stones were convex on both sides (just like ishi stones).

During the Ming dynasty, crafting skills progressed and stones could be shaped with 1 flat side and 1 convex (good for stability).

Japan imported the game of Go during the Tang dynasty (at that time the stones were all convex on both sides) and since Japanese are attached to their traditions, it stayed like this until now. (Which doesn't mean that the quality is inferior, it's just to stick with the tradition.)

With the years it also became fashionable.

For some people, Japanese stones make a better sound on the board, are easier to manipulate or are just pleasing to the eye. For others, Chinese stones are more stable and can be used on both sides to make temporary moves.

source: http://zhidao.baidu.com/question/265925385.html

PS: To answer your last question, the use of those stones is absolutely not in decline.