Well, that’s a special agreement then. *G with any *A Carrier usually does not work, EBG on any *A carrier works always.

Priority security screening is listed as a Star Gold benefit by the alliance:

https://www.staralliance.com/en/recognition

(Most) OAL*Gs flying SK don’t get SK priority security screening at CPH, even as *Gs flying SK should get the same priority screening benefits as SK*Gs flying SK given the priority security screening is listed as a *G benefit. But SK doesn’t do it in a way that is consistent with the Star Gold benefit for priority screening.

That’s all correct, unfortunately.

Priority screening used to be listed as a benefit without such “branding” and associated limits, but it seems like the alliance decided to re-package things so as to allow its members to continue to play consumer-unfriendly games while still having the alliance group advertise priority security as an alliance status benefit for those above the alliance’s first elite status level.

They may say that there are lies, damned lies and statistics, but they should have said that there are lies, damned lies, and advertising/marketing.

Getting back to why SK doesn’t want to operate an official Gold Track, I suspect it comes down to money in the end (as always). Of course SK would never let non-SK elites on non-SK tickets go through their fast track without getting paid from the airline; some airlines have then made a deal with CPH Express, and some, such as UA and LH (for non-HON), haven’t.

So if I were flying LH in J from CPH via FRA to wherever, I could either book directly with LH or as an SK codeshare. Presumably if I booked with SK (even only as a codeshare), I’d be able to use SAS fast track. And similarly, if I’m flying UA from LHR, I’d do better to book the itinerary with SAS than with UA (even though I’d be on SK metal for the first leg in either case). This is of course assuming that it’s the flight number that’s the determining factor, not the metal; I haven’t tried it, so I don’t know if this is the case.

Also, if SK were to operate a “real” Gold Track, even if it could get the airlines currently paying for CPH Express to chip in, presumably UA, AC etc. wouldn’t be interested; so someone would have to pay for the cost of their elites to go through.

Why SK still want the dedicated fast track in CPH is a mystery to me, but it might be because star alliance still consider CPH to small an airport for a proper *G gold track, the additional money SK has to pay for the dedicated SK fast track isn't much more than what they would have to pay if it was merged with the CPH express security check, and finally the security check area in CPH has been way to small for years. The security check area expansion was finalized recently, so if CPH manage to have a summer without long security check times, we might see SK dropping the dedicated fast track in CPH by the end of the year.
CPH airport is probably not interested in any changes either, as they are getting a lot of money for the different airlines for use of the CPH express track.