Depending of course, on what time this actually happens, I can see this being more the Church's bit than something that happens in any one kingdom or another. China developed this because it has a long history of centralized, top-down rule. Medieval Europe was pretty much the opposite of that. Individual lords and nobles could in many cases be significantly more important than the king of an entire "country" (term used rather loosely here) depending on the circumstances. These are circumstances that are more favorable to the development of pretty much what happened IOTL: networks of feudalistic patronage, ruling an efficient state was less the issue than making sure relations with all the important families and people were in order.
The Church is pretty much the closest thing that medieval Europe had to a central institution, and even that didn't always wind up working out perfectly (the clergy in Spain, for example, would obviously be concerned with different issues than the Papacy in Rome), but that's pretty much the best that can be done. And to some extent, the Church had things like this when it came to the rigorous monastic orders, many of which expected extreme commitments from their devotees in order to be allowed to join.