Remember that if you kill a Knight, the power goes to the next suitable "vessel". This was another reason why she didn't kill Slate. She wanted Harry as a Knight and needed him to be there when Slate died.
No.... That's the Mantle of a
Queen, specifically, it's only said about the Queen Who Will Be/Lady.
In SK the Mothers inform Harry that when a knight dies, the power flows back to the nearest Queen.
In CD we again hear that the mantle of the Lady jumps to nearest appropriate vessel, but we are also told that the mantle of Queen (Who Is) instead flows to the Lady (presumably dominoeing the Lady mantle to nearest vessel, as if she had died)
So, my interpretation of the flow of Mantles:
Knight goes to nearest Queen, for redistribution.Lady goes to the nearest vessel, no conscious choice involved (as we see in both SK and CD).Queen goes to Lady, ousting the Lady mantle.
Mother goes to Queen, again dominoeing the mantles.
Bolded is supported directly in text, rest is assumption/extrapolation.