Starting Kings aren’t going to have much fun. Maybe don’t start with a king at all. On d4 the court votes up the first king with whatever royal bloods that are still alive and step up. It lets the silly BD think they are voting up confirmed BD king without instantly murdering the first king for no leads.
This will encourage more deduction and proper logs. This will also help the proposed new king changes. Order will be more useful mid to late game when you are more able to deduce evil.
Having a king start later will make it more fun for the future first king and have a reason to choose between guarding or vote blocking depending on the King alliance. It will also give converted scum a chance to present their awesome fake logs to fool the BD into voting them up.
edit:
I don’t think not having king would go away from the base idea of ToL. In fact, it could be considered lore based as well. 16 people wake up realizing their king has been murdered by an evil faction. Now they must appoint a new king and root out the evil doers.