Something CK2-like ("sim RPG"?) had already been my hypothetical mobile game concept long before I even discovered (and immediately fell for) CK2: Macromanaging a player character that is basically just another NPC existing in a few layers of abstracted off-screen simulation, a slightly interactive story generator. Highly hypothetical of course, no way I'd ever make it a reality.
For example a pirate game would have a detailed social sim of the crew, an "FTL level" sim of the ship in combat, a "Sid M. Pirates" level sim of ship to ship combat (that is all NPC off-screen when the player character isn't in command of a ship) and a sim of baroque-era Caribbean economy. A low level sailor would just manage relationships and balance focus between categories like following orders, initiative, camaraderie, bravado and risk avoidance (each influencing how he fares in the off-screen social and "FTL combat" simulations), peppered with the occasional decision set-piece, whereas a pirate-king might decide on resource allocation and strategic city upgrades (but still not micro-manage anything but relations). The tactical level would be a much more interactive (if the PC happens to be in command) series of decisions, but still do exclusively fast-forward-to-pause timing. ("free form turns", imho mobile games should be as passive as a book whenever you put down the phone)
The pattern could be applied to anything that has a somewhat limited set of characters for the social layer (the CK2 courtier population might still be a bit heavy for mobile...) and involves separable tactical and strategic layers. The original idea came from the question of how one could do a WW2 air combat sim on mobile that is deeper than Sid M. Ace Patrol but unlike IL-2 still without a dexterity factor. The player would balance focus between e.g. spotting, engine operation and navigation when on mission but not in combat and during engagement between aiming, evading, energy conservation, situational awareness and so on (plus a series of decision points that might be seconds or minutes apart depending on situation). The social layer might involve storytelling decisions like choosing to "accidentally" miss an emergency scramble after a night of heavy stress relief or flying under the influence.
With a bottomless fantasy budget, this kind of game would come with full 3D modeling for illustrating every sim layer, but only ever show a single frame at each interaction, representing the state of the simulation (which is actually closer to board-game abstraction than to 3D physics) in a semi-randomized way. Reasoning: animations quickly get old no matter how good they are and single frames can be doused in nice-looking postprocessing that would cause unsightly artifacts if animated. An endless pool of informative flavor illustrations, not the usual showing-off of GPU power and production effort.