In London airspace, In the North Sea sector (that controls a tiny bit of the airspace over the North Sea), I haven't seen or heard of anyone doing this.
The North Sea Reduced Coordination Area is designed to allow GAT to be sent direct as much as possible when the D323 complex is inactive with the responsibility of coordination between the Mil and civil controllers falling on the Mil. It is also important to remember that it only applies to a small proportion of the the North Sea.
During published hours of activity of the TRAs it applies from FL245 upwards and outside of those hours FL195 upwards. Maybe during the hours of activity the controller(s) is using the phrase "due to military activity" as an easy way to explain why a DS is being given. I would expect you to get to get a RCS above FL195 within the TRAs when they are not active ie the weekends and after 1700 local. You certainly would in London.
As Scottish controls the vast majority of the north sea and I don't work there then I can't speak for them as to if and why this maybe happening. There maybe some reason for it that I am not aware of.