This is a hot topic right now.  The best way to address this is the most obvious:  allow offspring to ascend to the throne.  If there are no offspring, then the kingdom should either go neutral or have a NPC hero take over.

This issue really needs to be addressed ASAP since it is hamstringing a crucial game mechanic (dynasties). 

there should be neutral cities, like in Master of Magic

Aliens....

if all else fails aliens are a great excuse.

One idea would be to check if there are champions in those cities, grab the one with the higher overall stats and have them take over the cities.  If the Sovereign had children, they should have an opportunity to take over if they're not in the captured city.

I imagine that they don't have code in place to generate a new kingdom, empire, or minor faction on the fly in the middle of the game.

There's a great opportunity to make the champions / dynasty interaction work here.  If the sov falls, whomever is left should try to pick up the pieces to keep the kingdom going, but not the entire kingdom.  An enterprising champ who's squirreled away in a back corner may suddenly decide to go independent, and a new neutral city is formed.  All those +10% production and +20% farmers come to mind.  The spouse of the sov and any kids would probably try to stick together, unless that spouse is from another empire - loyalty to that family might trump their adoptive home.

It's not a fun situation to dig out of, but it's better than losing the game outright.  Plus, it's pretty freaking epic to have a large empire shattered when the king falls, and the remnants avoid notice long enough to recover and get revenge.

The idea of such a cool feature missing from the final game makes me sad... Does anyone know why it has been excised? (did I spell it correctly? excised? )

Wow, my Italian Blood demands some love affairs "Faida" then!