I’ve never noticed such a pattern myself and I’m not sure I’d agree that most kings are depicted as red-headed. It would be a little odd considering the relative rarity of red hair in people. What specific depictions are you talking about? Could you give us a list of examples? If you google “cartoon king”, you’ll find only a few redheads among dozens of brown or white-haired kings, which is what I’d expected to find. Maybe if this is a legit trend you see, it could be regional thing? Are there many red-headed people in your country?

I have never made that sort of connection. Fictional kings? IRL kings? Sacramento Kings?Can you give some examples?