Bottoms Up
The government in Taiwan was the government of China when the registration came into being. In fact they still consider themselves the government of China.
The mainland government doesn't see it that way and uses the prefix because they consider themselves the government of China.
Neither government recognizes that they are two different countries now.
We probably won't see either side give in on the registration issue as that would lend validity to the other's claim of being the legitimate government of China. It would also mean admitting that there are now two seperate Chinese states.