And you know how many resources have to be diverted to all that training?
Resources that could be making them more effective soldiers (combat penalty)
Resources that could be making them better at raising their own family (growth penalty)
Resources that could be making them better workers (gold and production penalties)
Sometimes resources that are necessary to make sure that your citizens and troops can properly identify friend from foe (rebels..even city flips, as they might accidentally see other immortal leaders as no different from you, and therefore accidentally switch loyalties)
And more of those resources have to be used when you take over new territory.
Multiple things can make the training easier,
ways of distracting them (luxuries)
self-perpetuating ideas (religion)
various forms of infrastructure can be adapted to more effective use of local training resources. (buildings..sometimes with social policies)
[ps I agree that stability would be a better name]
You forget: The SS regimes, North Koreas current training programs, Sparta, the Mongols and half a dozen other warrior cultures and or special forces.
As to the resources you say to me about lets talk to our minister of propaganda, he has this to comment:
"Our army is well trained and equipped. Every unit that takes to the field spends time in our training facilities for about 5 to 8 years before seeing actual combat (IN GAME: Barracks, military academies etc. 5-8 turns in production

). Our soldiers are trained from infancy to be the best at what they do (NO FAMILY- Warrior caste from the Honor tree) and they are completely dedicated to the cause. The rest of our citizens occupy the best positions (specialists/fabricators/whatnot) due to higher training and absolute loyalty to the cause. The menial tasks that are required for us to preform are done by the as of yet non citizens of our empire (AKA Slaves captured in war). But rest assured, when their tasks are complete for the day, they spend some time on our education programs. In the future they will understand the benefits of our great civilization (sic) and will be rewarded with citizenship themselves. Rest assured that with the advent of robotics propagated by our great scientists, necessity of menial tasks will be eliminated in the next half of the century (I foresee food reductions....)''.
Spokes man from the army general whatshisname had this to comment on the matter of loyalty:
''The way of our empire, is the only way for mankind to traverse forward. This has been engrained into our great civilizations psyche since the day our great leader appeared to us. He led us to become from club wielding savages, to an enlightened empire that has spread its ideology through the world. There is no corruption to our state, there is no jealousy, there is no ugliness, there is no evil. There is only a uniformity of destiny that belies our purpose: To unite the world and end all wars under a single banner. Only then will mankind truly prosper. The other leaders...They waste their time calling us warmongers and other things, yet they have yet nothing to show the world. Their nations are week, malnourished and filled with unhappy souls that care only to ephemeral pleasures to deny the reality of their everyday lives.
No there is no other way for us, the worlds corruption must come to an end. All we need is our martial code, discipline and our weapons. We will rest and enjoy ourselves only when we bring final peace to this world''.
TLDR: If you brainwash a nation day in and day out since the day they are born, there is nothing to distract them.
Also take note that you started this as how it would work inside the game and propose mechanics outside the game: There are no special resources needed for your troops in the game to preform their duty, and there is no loyalty factor. They need the maintenance costs and whatever else special it requires to produce them: Loyalty factor, no payment, No questions asked. The dream army of the insane dictator

There is no need for global happiness reduction. I would say not even local (after all who asks the occupied citizens if they are happy?) but I would agree that local happiness must be reduced.
Sounds like a paradise; how much are the tickets?

Free as long you are brainwa...I mean take tuition by our dedicated Civil officers before you come to visit. We accept tourists only on certain dates and under certain conditions. Come join us and make our empire proud! Be sure to buy the tourist souvenir that plays the national anthem 24-7, a poster of our illustrious president, and the new Mk6 assault carbine replica used by our forces on the front.
*We bear no responsibility for maiming or deaths incurred by the weapons sold to tourists, and certainly not for any defections to our glorious state. By visiting our glorious empire you agree to these terms and conditions, as well whatever you will find on the assorted documents handed to you to the foreigner receiving office.
EDIT: Just read that:
Happiness is a warm nuke bath?
I had our environmentalist department head (YES we do have one, we are not heartless b...) for a comment:
'Urhm...We dont use nukes....Erhm, they hurt the planet?'
Our scientific adviser also has this to say:
'Since India threatened us to a peaceful nuclear exchange the last month, we started construction of a spaceship which will lead a portion of our people outside this planet. Once this project is completed any threats that imply use of nuclear weapons will be countered by use of the mutually assured destruction protocols'.