If EK were to base crews in CPH, they'd run into the exact same issues as Ryanair. Namely that some incredibly powerful unions will insist the airline signs a CLA with the based crews under Danish law. Should EK, like FR, choose not to do so their flights will not receive any ground handling.
The case agains FR has been in the labour court, and a ruling is expected shortly. Whether the ruling goes for or against the unions the result will be the same: Either a legal or illegal halt to all ground handling. FR will then either discontinue service to CPH all together, or drop the base and only serve CPH from other stations.
FR will never sign a CLA under Danish labour law, and I cannot fathom a scenario where EK would either. As with FR, the repercussions will undermine their businessplan to the point it no longer makes sense.