As it currently stands, children don't serve much use, and add essentially nothing to the overall gameplay experience.  This, in my opinion, could  be rectified by making your heirs actually capable of inheriting the kingdom and the channeling powers if your leader should die. 

There are a variety ways in which this could be implemented, I believe, so that it doesn't result in overly long games because your enemy has 20 heirs, and they're spread throughout the world.

I was thinking that one could have a spell, similar to the transfer essence spell, but usable only on your children, more complicated to cast, and perhaps require some research.  Once the essence is transferred, it means that the child can now inherit his parent's channeling powers should they die, and have access to spell casting.  A kind of heir designation spell, if you will, that can only be for one person until they either succeed to the throne or die, and can only be used on your children, so when your heir does succeed he can't use his brothers or cousins or whatever as potential heirs, only his direct children (assuming they're old enough).

When your sovereign dies, there would be a time period in which your heir was then moved to the capital and incapacitated for as long as it takes for him to absorb the powers of its parent. 

Since many players have stated that they do like the fact that they can survive almost certain annihilation by killing a rival sovereign, instead of making it so that their kingdom is destroyed, why not simply have the AI offer peace immediately after their channeler dies (which you can accept or reject), while they adjust to the change in government.

Another idea I have is that instead of computer cities being destroyed when they have no channeler, give the option for some of the cities to join either you, or rival kingdoms, as a way of making the gameplay and strategy more interesting.  I presume that an empire/kingdom cannot exist in Elemental without the aid of a channeler (as they bring life to the lands... or shadow... or whatever their people need).  So if cities face almost certain destruction because they don't have a channeler to support them anymore, then you'd think they'd try and find one, and beg them for protection.  If no one accepts their offer, then the cities should be destroyed.

Well I don't know if any of these ideas are worth mentioning, but I thought I'd put them out there, just in case there's SOMETHING that's usable, or something that's capable of inspiring even better ideas.