PanAm had to give up their flights to Taiwan when they first returned to China in 1981. The original flight was a 747SP doing NYC-TYO-BJS-SHA-TYO-NYC triangulation.

United didn't have the problem as the US didn't have a designated "flag carrier" after PanAm went bust. The Chinese government only required a separate entity to operate to Taiwan if the airline is designated as a "flag carrier" (thus NH and OZ never had to do anything weird like this. Ansett also flew to TPE under its own livery without issue, while also flying to Shanghai). Northwest Orient kept TPE routes after PamAm dropped it. This rule had not been rigorously enforced since the mid-2000s and was officially abandoned by CAACsometime around 2010 or 2011. KLM had a few 747s flying around with "Asia" livery until just a few years ago, but those were not necessary anymore - they just didn't repaint them.