Two points to make here:

1. Yes, it's possible to paint a different name on the aircraft. But then EK would have to ensure that particular plane served TPE ... not an easy task given its large and varied fleet.

2. In the days when British Asia Airways etc were set up, mainland China was a sleeping giant and nobody could have foreseen how the country would expand so dramatically.
Given the prickly relations between the Beijing government and Taipei and given that traffic rights to mainland China are always a political issue ... is it worth an airline jeopardising its expansion plans to what will become one of the world's largest travel markets for the sake of serving a single destination, ie Taipei ?

Point taken. It's been worthwhile for other airlines in the past, and given either CI's or BR's only basic coverage of Europe/Middle East, Emirates could do very well. BTW why can some airlines fly to TPE without any name change, the likes of SQ, TG, MH ?

Good question and, by the way, UA would be another example.

I don't have a definitive answer. All I can suggest is that the carriers mentioned above have all been operating flights to TPE for several decades without a break. So I guess they've become established on this route.

European carriers, with the notable exception of KLM, never considered serving TPE until later.

KL continues to serve TPE but the other European carriers who served TPE (LH, Swissair, BA and, maybe AF too) only served the island for a short period. One by one they cancelled their TPE services claiming, if I remember correctly, they weren't viable.

But was this excuse really true or was there was a political motive ?

IAH has been mentioned as the possible next USA destination. SFO or LAX as well.