the problem I think is that the cheater AI is unstoppable cheating -- his cheating becomes almost independent of his state within the game (true independence is the behavior of actual cheating), such that your path to victory really ends up being complete and total domination. You can't really apply normal strategies like crippling the opponent by poking the edges, or baiting a fight here and having a small force go around to there, or focusing down the infrastructure over the army itself; there is only the main body, and that's all that matters..
I think cheater AI is probably a perfectly good strategy; its just the implementation is never done that well, and it ends up cheating in a fashion that isn't actually interesting.
Alternatively, the cheater AI could simply be given an aesthetic reason to validate cheating, instead of trying to pretend its a normal player -- eg AI war simply defines the AI as an overwhelming force; so overwhelming that it doesn't actually pay much attention to your activity, and that's the only reason you're not dead (your goal is to continue growing without letting the AI noticing).
Total War and other 4X games generally have you playing where the AI is also generally unintelligent, but feels more fair, because everyone is in various starting states of strength. The cheating AI gets a set of arbitrarily strong units, justified because its simply a strong country 10x the size of yours. And then the amount of blatant, uninteresting, cheating that has to occur is much more limited -- if the AI is not sufficiently challenging, then it's generally simpler to increase his relative size, or resources, or production facilities, or whatever. What the AI does after that, after the game has started, becomes less important, so what cheating occurs becomes negligible from the perspective of the player. A 50% cheating bonus to production time doesn't mean much when he already started with a 500% bonus in resources and production.
Games like MoO and Civ make the mistake of having everyone start at the same state, even when its just you vs the AI(s), because they don't treat the two differently -- there is only one setup, one goal, one victory condition, regardless of the number of human players. That is, they don't admit to the weakness of their AI, and try instead to make up for it "under the hood"; and when you as the player catch this cheating, and it's never that hard to, you feel inexplicably stupid to have ever thought you were playing a fair match, and losing/winning to fair rules. The same as when you catch a human cheating.
Most other 4X games are defined as you vs the AI, and there's little to no multiplayer in the first place, so the idea doesn't trivially translate, but you vs the AI should probably be treated differently than a legitimate multiplayer map anyways -- as a campaign setup or a skirmish map.