Both the Republic of China (KMT) and the People's Republic of China (CCP) claimed to be the one legitimate government of China after 1949. So recognizing both wasn't possible. I know Taiwanese independence is a hot-button issue for the PRC, they said they'll go to war if that happens so that's basically off the table.

I also don't think North Korea was given diplomatic recognition by the US, if memory serves the US to this day handles it's affairs with North Korea through the Swiss, they have no embassy in Pyongyang. That might also have been the case for East Germany.