In this thread, it is mentioned a few times that a city producing highly promoted units isn't very useful to the AI because it doesn't protect them well. I strongly disagree with that. If I have a city that can produce 10 XP units, then I will use these troops. No, I won't use them to attack at 30% odds, that's what siege units and bombers are for, but the AI typically won't use these units for that job either (as explained by jdog5000 in post 13). But I will use them to attack at 70% odds when my lowly promoted units have 30% odds. I can produce more of them so they're not irreplaceable and I won't lose them as often as lowly promoted units meaning that I need less production power to win a war.
If two stacks of the same units meet, one promoted up to combat II, the other up to combat III, then the higher promoted stack will incur less than half the number of losses of the lower promoted stack in the ensuing battle. That's how dramatic the effect of even one measly combat promotion is on battles. And there exist far more useful promotions than the combat promotion that can be chosen.
Now there is a limit to the usefulness of adding Great Generals to a city. For non-charismatic leaders for instance, going beyond 10 xp (3 promotions) is not extremely useful. It takes 3,5 GG to go from 10 XP (3 promotions) to 17 XP (4 promotions). For that investment, you could also raise the experience level of another high production city from 3 to 10 adding two promotions to the units produced in that city. For charismatic leaders, you could argue whether 8 XP (3 promotions) is enough or you want units at 13 XP (promotions).
The AI should be aware of the minimum xp levels needed to reach a certain number of promotions (2, 5, 10, 17, .. for non-charismatic leaders, 2, 4, 8, 13, for charismatic leaders) and try to get to some threshold level of experience when it is using it's peaceful, non-war civics. If the AI can also be taught to create military production cities, then these cities should also be producing highly promoted units in peace time. The war-civics are mainly useful for the other cities that don't have great instructors.