If you accept the fundamental principles of openness and honesty in public office, then anyone being presented with, or asked to endorse, an NDA will be required to compromise their personal integrity.
NDAs are fundamentally required to cover up or avoid publication of a set of circumstances.
How can that EVER be appropriate when measured against the NOLAN principles.
So that would be my starting point.
Now to the reality of joining a PC that has (IMHO) inappropriately agreed to an NDA (a) because it suits them to seek to prevent scrutiny of the inadequacies of staff management and scrutiny leading to the reasons for the staff member having their contract terminated and (b) to facilitate a payoff and avoid the potential of a constructive dismissal and not have to explain this to the public. Another issue is that it may include a stipulation as to future employment references so that a known incompetent, liar and manipulative deviant can continue their rein of moving between councils employment and continue the charade generating chaos and harvesting pay-offs along the way
If a PC needs an NDA there are likely to be fundamental issues which the PC wishes to avoid publication.
I cannot think of a valid reason why an NDA should be applicable in public office.