> One of the most dangerous things in government is making a cult of personality around the head of state. Having it be a powerless figurehead takes the bite out of that.

Not really. The cult gives its focus power regardless of the formal structure; that's the point. And in the case of England, the formal structure still supports the king! Forming a personality cult around the King of England is more likely to lead to the King of England reclaiming a lot of power people thought he had lost long ago than it is to defuse the cult when they learn the king isn't supposed to use his formal powers.