So if you refuse to listen to the Hunter then you die.
While if you refuse to listen to the King then not much happens.
If he gets enough votes to put you up, he can kill you with decide fate. If he can’t get enough votes, in some niche situations his point finger is enough to guarantee your execution. Even in general, the court is usually willing to put someone up who has had the royal finger pointed at them since it’s considered a sign of trust in the court’s judgement and the court is always more than happy to judge a case.
The point being, King has more power over daytime trials than Hunter does which is the same a King being better equipped to lead.
This is largely why the King whisper meta exists - to give the person best equipped to lead daytime trials the information to inform the way he uses those abilities.
If King isn’t fed information, his abilities are fairly useless since he won’t know how to use them. He would be either randomly pointing fingers or just sitting doing nothing at all.