Um they are still kids and kids don't usually have high stats you know? and why would a administrator be Needed?
The only mention on the stat sheet for immaturity is Gwen's -4 martial. I'm not under the impression that passive stat growth is a thing for them.
As for why we might need someone to be the full time king/queen of griffonia as opposed to being king/Queen and emporer/empress in one: well firstly they're two different jobs, secondly both are going to get more complex as time goes on, thirdly it's not good to focus all your training on the primary heir because that not only breeds resentment but also means you're left with weak candidates should something happen, however training them well means you have multiple qualified individuals in need of employment so having the government of the capital province be separate gives them something time consuming to deal with, this also takes pressure off the imperial crown so they can focus on the overall big picture.