I disagree because, historically speaking courts in feudal countries have often been dependent on which dynasty was in power and even then moved around a lot. The AI should desire provinces and duchies based on an estimate of their value and try to take provinces that would be valuable to it, if it has a convenient way to do so. And in the same vein have a set of weights for where to place it's capital.
I agree.
Obviously you can define capital significance in different ways - as a holy site of coronation, center of power, center of trade/wealth, culture and so on.
Not sure how a game can model all this, so system of weights and values makes sense, perhaps with coronation points, trade points, culture/learning points, power base/ducal inheritance points. Then these points could either justify creation of a capital or somehow be turned into extra bonuses upon conquest, providing some incentive to move capitals if there is de jure claim.
To give some examples,
You have Aachen very deliberately chosen by Charlemagne for the Carolingians, with administrative counts and missi projecting legal authority throughout the realms.
Then the Ottonians (and later kings) coronated there, Otto I moved from his power base in Saxony to Italy, which didn't go so well, and then he had to face a civil war and revolts back home.
After feudal cellularization,
In France, notably Reims, which Charles VII retook from the English, allowing his coronation there, quite a big deal.
You have places of great investment and learning/universities like Paris for Philip Augustus or Prague for Charles IV.
You have Frederick II who went on crusade, and based his power in Kingdom of Sicily and Italy, not Germany.
Then valuable possessions that could in theory become capitals such as Sicily again, divided from Naples by the Aragonese and ruled by Frederick III, or the Low Countries and Bruges as economic capital vs Brussels as court for the Burgundians, or London vs Westminster.
