So much of this fits under "marketing our value to rest of the org" - which to me (who is convinced democracy matters) says the organisation is lacking ... journalism and open fair competition of ideas.
Having the best idea reliant on top / upper top managers spotting the best idea is ... not great. And I am not convinced that having a "good communicator" as the solution - because what if the well connected manager is on the poorest product solution?
As for the rest - yes google has 8 whatnots for managers that read as a coaching manual - its important yes, but I would be astounded if there are not better things to focus on.
If a good manager is like an army sargeant, who are the colonels and generals? Where is the operational plans? Maybe I just get kept in the dark and fed shit but an open and coherent communication will get people aligned without being micromanaged