Don't think it's very gamey. Didn't Ottomans make eunuchs their bodyguards and administrators too? I mean, breach of feudal contract boo hoo. If it works, it works.
If there are both viceroyalty administration laws and a Culture of having eunucs do the administration, and even then it might still be deserving tyrranny. Still, if you are the king of France then there is no way that I would buy that one could do that.