I use dumb questions a lot as a manager - although my hiring intentions are to try and make me the actual dumbest person on the team anyway.
I don't use it so much for the teasing out agreement or highlighting problems angle though - one of my goals is setting the accepted threshold for dumb questions low enough that junior/newer or less confident team members aren't afraid to ask their own "dumb questions". Those questions are usually more important than mine, and teams that don't have that "no question is too dumb" culture are often dysfunctional or heading that way.
I don't use it so much for the teasing out agreement or highlighting problems angle though - one of my goals is setting the accepted threshold for dumb questions low enough that junior/newer or less confident team members aren't afraid to ask their own "dumb questions". Those questions are usually more important than mine, and teams that don't have that "no question is too dumb" culture are often dysfunctional or heading that way.