I dunno. It seems far more thematic for a Conqueror trait - you let them have the administration of the capital city, you handle the main administration of everywhere else and all the effort goes to somewhere.
A lot of it is mainly because there is no such relic system. I'd actually be inclined to create one - python scripting it right? If there's a function to handle discerning if that was the enemy's last city... I could probabaly roll it out pretty fast. Ideally, it'd be a choice for the conqering civ of the three palace mana that civ spawns with, through an event, then it drops the relic which is just Conquest Mana: Law, or somesuch that can be put in YOUR capital.
Alright, now I've gotten myself exited. Is there function for "last city of X civ, run event code X"? Or a nudge in the right direction?