In real world, kings/emperors have led their troops onto the battlefields since time began. Sometimes with glorious outcomes, and other times with disastrous results for his country. But this is part of the "epic" feel of strategy game. If the user or AI wants to risk Sovereign, then they should be allowed to, as long as there's sufficient pro/cons to consider. Then they have to deal with the outcome. That's all part of the gamble that makes game (and real life) interesting. This is a part of the game complexities that was not implemented well, but could be fixed to greatly benefit the game.

Also in real world, "leadership strikes" works wonders. (as was done in Iraq and WWII). Disruption of a country's leadership is a legit tactic in war. This is even better with assassinations, though it's much harder to implement. If you guys have ever played Star Wars: Rebellion, it's a 4x Space game, but not that great (but SW theme makes up for it). There's one part that's particularly fun, and that's assassination of NPC or heroes. Just imagine if you can do similar things in this game. Also assassinations would allow more RPG like atmosphere in this game,

So I definitely think Sovereign should be killable in battle, it should be done so with high difficulty, think Sauron-type difficult. Or Sovereign should be beyond the ranged weapons so you have to wade thru his melee troops before getting to him. There's nothing more inspiring than having the leader of the country leading his army to siege the enemy. The AI does not have to do that, but it could be allowed to do so with some benefits to the attack/defense of the army he's leading (again, think Sauron-like leader that leads his hordes).

As for dealing with the aftermath, this is actually an OPPORTUNITY to make the game fun. First, the country should definitely not fall apart. This is a great time to use the Dynasty system in the game (and in real life). Without a way for succession, then you miss out one key part of how a dynastic empire works. What good are kids if they cannot take over after you? When Sovereign's killed, if there's a queen, she can take over. Or if there are kids, the AI could designate a regent until kid grows up. And if you really want to get complex, regent can initiate a coup (maybe even with support from user or other AI), then you end up with this new leader, and the leader may be more favorable to one side or another. Alternately, the AI could simply create another Sovereign for the remaining part of the empire, just think of as if someone (some previously nameless general or governor) rose up to fill the power void right after the Sovereign's killed. This happens in real life, and it makes the game that much more interesting.

As for how to implement it, it could be as easy as a global event message after the original Sovereign's death..."so and so became Sovereign of this place". Or this can be made much more complex, with political intrigues mentioned above. And as a penalty to loose Sovereign, then you can institute a penalty on the attributes, mana, gildar or whatever. Again, think the chaos in Iraq after government fell, people looted stuff, destroyed infrastructure, so it's reasonable to have a chaotic period. The user/other AI could take advantage of that, but assuming the rest of the empire is intact and with sufficient military force, the new Sovereign should be able rally the troops and repel the invasion, or at least save the core parts of the country after loosing some territory. It is only with overwhelming opposition would you be able to roll over the rest of the territory. And then the new Sovereign would build up again and strike back. All this "ebb and flow" is what makes 4x strategy game fun and interesting, you don't just steamroll everyone, especially in the end game when things get tedious. Just like in a prize boxing match, it's the most exciting when you have a stubborn challenger that keeps coming back and trades blow for blow, then then finally fall in a glorious fashion. This is what makes the game fun. I feel this part about dynasty system should truly make Elemental a unique game that far surpasses other fantasy 4x such as MoM, AOE:SM, HOMM and Domination3.