While thinking about the issues with ACKS' domain system, I keep returning to Renegade Crowns. It's strange that I mentioned it during my Suns of Gold review without making the important connection.
Suns of Gold has a trade system that generates adventures - you often have to go on an adventure in order for a deal to be profitable. This is good, and fun!
Renegade Crowns' domain system is also designed to make domains a source of adventures. If you want to stay in power, you have to do stuff. This is... good, and fun? Probably better, at least, than "I sit back on the throne and send henchmen".
Notably, RC has a "domain engine" (sort of like a world engine, but smaller). It has two pieces of state: an Internal Trouble score, and an External Trouble score. These go up over time, and going on adventures can reduce them. If they hit certain thresholds, mandatory adventures happen - deal with them or be deposed. Internal Troubles may result in settlements declaring independence, peasant rebellions, or courtiers assassinating you, while External Troubles might be monsters eating your peasants or neighboring domains declaring war and invading. Solving these troubles has varying effects on the trouble scores, depending on how well they were solved and by what means (for example, brutality tends to project strength to monsters and foreign powers, but breeds local resentment).
While the specific modifiers to trouble scores are rather... cynical ("If the characters actually solved the original problem [causing public discontent], increase the Internal Trouble score by 5 points. The population now knows that they can get the prince to do things by complaining about him, and they are likely to try it again in the future"), in the Warhammer tradition, something more-or-less of this form is probably a good replacement for Morale for Simple Domains.