Without it dong anything tangible to benefit the player, I think this is a worthless idea. It is an interesting number that everyone will look at for a day or two, then forget about and ignore. Kind of like the top family rankings we already have.
If it is somehow turned into some kind of system with a tangible bonus, then it will need to be tightly researched, designed, and controlled so as to prevent abuses. Some kind of continuous bonus like Anaris mentions is infinitely more balance-able and less prone to abuse than a point-spending idea.
However, you also need to evaluate the possible negative effects this could have, too. Off the top of my head, this provides big incentives to not create new duchies, and thus centralize power into the government to a greater extent. A single duchy realm with everyone together would provide the largest number of nobles for the duke, thus giving the duke the highest possible continuous bonus to spread across his duchy, and thus the biggest benefit to everyone in his duchy (i.e. the realm). So, why make more duchies? Reduced duchies leads to reduce intrigue, reduced opportunities for secession and allegiance changes, betrayals, etc.
