...why?
Mafia can just lie. You gain no actual information.
Of course we do. Everyone
should be giving their roles to Demonslayer.
If anyone CCs a role, then we know one of them is Mafia. We can choose to lynch them now, or wait until later when there's fewer Mafia and thus more to be gained by sacrificing power roles to kill them. The choice is ours either way.
Say we have this scenario: One Mafia claims doctor. Now we know that one of the three people who claimed doctor was lying. However, lynching them is not in our favor.
Not right
now it isn't, but if it gets down to 1 or 2 Mafia left and there are 3 people who've claimed Doctor, it is certainly in our best interests to start killing them off. If it comes to that, the King can name one at random and we lynch them.
Worse yet, one doctor forgets to claim, and now the king thinks a mafia member is doctor.
1) If one Doctor "forgets" to claim, then he's a bad Doctor and will probably "forget" to protect people too.
2) It's not like the King is going to tell him anyone else's role. The Doctors should, at the very least, inform the King of who they are protecting/shielding each night. If one Doctor is protecting, and the other is shielding, then the person becomes vulnerable to normal hits. The King could then tell the person who is shielding "You need to change your target to someone else."
If the King is confident they are legit after a period of time, he can direct them to protect specific targets.
Having more information is definitely for the best. The King can decide what to do with the information he receives depending on what happens in the game and any inconsistencies in said information.
By claiming power roles, mafia members can almost completely shut down the information gained by the king.
Better to have some wrong information then no information at all. The King will of course be aware that one of them is lying, and can handle it accordingly from there. If it gets near the end of the game, when there are very few Mafia left, then the Mafia who lied has committed suicide.