I think the challenge of the peacetime gameplay loop is exactly that it's not very good to interact with as is, not that it isn't detailed enough.
If you look at laws, tech trees and religion, they exist to reward you with bonuses for clicking on them or to unlock parts of the game (legions, certain upgrades or systems) that should be unlocked anyways. More buttons will mean more bonuses I guess, but not sure how it would change anything in the grand scheme of things.
The other peacetime gameplay that isn't player initiated comes from the generic events (another corrupt governor, another pervert officer holder can be fired, another slave revolt can be avoided entirely with a click) which makes it stale exactly like CK, but for some unknown reason, just because it was like that in EU:Rome, they kept the same indirect character control that they were using in that game and Sengoku to experiment on, before coming up with the winning formula in CK2 and beyond, so you can't even keep yourself busy playing with your characters properly.
What the new game really needs is a mini-game like marriage/family management is in CK2/3 for the player to spend time on, only for politics.