One thing that I would like to see added is some way of simulating the communication difficulties inherent in this time period. Long communication delays were one of the primary causes of the disintegration of large powers. This wasn't just an issue for the movement of armies. Communication delays made it easier for regions distant from the capital to formulate and implement their own policies that may have conflicted with the aims of the central government. Distant governors could more easily establish their own base of support and authority within the territories that they ruled. Also were often assigned to governors because they were best positioned to rapidly respond to foreign incursions.
Obviously the player must take an unrealistic level of perspective in order to play the game, but you could simulate these challenges in other ways. Maybe power costs, times and likelihood of rejection or increased resentment could result from interacting with and overriding characters located far from the capital. In addition to commanders gaining loyal cohorts, you could also have loyal cohorts and cohorts under the command of a governor get bonus to movement speed or combat in the region to which they are assigned. With the addition of the coconsul mechanic you could add other dual ruler mechanics. like maybe you establish one of your sons or a close political ally as co-emperor in order to help with administering different ends of the empire. Sure it is now cheaper and easier to directly manage affairs far from the main capital, but you are also creating a secondary center of power that might one day challenge the government for leadership.
On dual leaders and civil wars, why should the game end because the main government under the player lost? Divorce the player more from the specific political factions by allowing them to pick sides in the civil war and continue running the country regardless of who wins once the war is over. Trying to lead the nation after it has just been through a brutal civil war and is now under new leadership (a leader that may not have been the player's first choice) can be a fun challenge. After all, just because the Shah's sun overthrew him doesn't mean that it isn't still the Persian Empire that he is leading. This would also give player's more agency in matters of succession by allowing them to push the country towards civil war in order to get rid of the incompetent twit sitting on the throne in favor of his much more brilliant older brother. Of course, that means risking losses to opportunistic neighbors, but hat is an interesting choice that the player may believe is worth the risk.
I agree 1000% with everything you said. And also will give roads more meaning if they influence the penalties related to distance.