The excuse in CPH has always been that the fast track did not have sufficient capacity to be a full fledged Star Alliance facility.

Lufthansa only offers fast track HON members in CPH, the rest of the passengers are sent to the standard lines.

For other airlines there is then the whole show of does TK *G on A3 Y gives access? Etc. etc. through the combinations of airlines and programs. It would be nice with an official Gold Track in CPH. But until SK give up on their own, and joins forces with the rest of Star Alliance, there is not going to be a business case, also I wonder where to find the space