Body doubles are used for setting lights, decorations, camera settings, crops and angles, arranging stage motion so actors don't collide with equipment or dolly tracks during shoot, adjusting audio microphones, line reading for extras and supporting actors, crowd rehearsals, etc - that kind of stuff.
It rare for a double (other than stunt double) to be used in the actual shoot of final footage instead of real cast, unless the actor in question is genuinely unobtainable at the time (dead or last minute retake while the star is shooting another scene on the other side of the world).
With shows like GoT main cast is usually paid per episode of a seasonal contract split into several tiers and it's also common for all of them within tier (main cast, main supporting cast, supporting cast, re-occurring regulars etc) to negotiate identical group deal regardless of how much time it takes to prepare as individual, and as you can imagine, within last episode production alone, Kit probably worked much harder and longer for his money than Emilia.