What are the advantages of ECTM and why is it not used in military aviation even though it will help in many ways?
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ECTM is, I would argue, a necessity for proper maintenance planning/efficiency. I'm not sure why you think it isn't used in military aviation, and I suppose I cannot answer for every military aircraft fleet in the world, but I can assure you that it is used in military aviation.
My answer may not be very complete, but the very short version is "If you don't measure something, you can't plan for it or make it better".
The main advantage is establishing a normal rate of degradation for the engines so that you can pick up on anomalies that suggest latent problems, as well as anticipate major overhaul points with better accuracy which is great for long term planning.
Three of the biggest items to monitor would be ITT margin (the difference between the peak ITT shown at takeoff thrust and the max ITT - when you are out of margin you are out of engine), oil consumption, and vibe levels.
As Capt Reynolds shows, I would expect that trend monitoring is common with penny pinching NATO airforces, but to the extent that military organizations don't use trend monitoring, I would guess that it's due to a "disposable" culture within the organization.