This may not be very popular, but when the sovereign is defeated in battle, I would like the down time to last a little bit longer. In addition, I also think it would be great that while a sovereign is unavailable, all of that kingdom's unit have some penalties in battle. Perhaps -20 to accuracy, minus -2 to attack, and -15 to dodge. Or even better, have the penalty based on the sovereign's level. Dodge -1.5*level, Attack -level/2, and Accuracy -2*level.
I read that the dynasty system is coming back, which I am really looking forward to. This would be a great time to add it and it could also be effective for any member of the "Royal Family".