That only works when the good and bad cops are independent, with no one subordinate to the other.
The scary mooch works for Trump. So Trump is responsible for the behavior and actions of his employee when it is during work hours and part of his job responsibilities.
No, it works when the top dog has an enforcer. That's why top dogs typically have enforcers.
And political/optical responsibility is not the same as a superiors legal liability for the actions of a subordinate.
Think of the cliche of the gracious mob boss who can afford to be gracious, and is respected as such by those he deals with, even though also feared, because he has his ruthless subordinates.
I'm not saying it's a management style to be emulated, and it is dependent on personalities, but it can be deployed and given the lions den of the civil service any republican president would find herself or himself in, might be advisable at this point in time.
The trouble is, Trump is simply too incompetent to carry it out.