It isn't a matter of whether a public entity can recognize a high-level manager's value; it is a matter of whether they dare compensate them competitively because of the politics of public sector pay, particularly in managerial and highly specialized positions.

In jobs that are only done in government skillful people can be retained because they're place-bound or held by the golden handcuffs of attractive benefits.   For jobs done in both the public and private sectors and for which there is no, or at least not much, partisan political vetting, they only thing that allows you to recruit and retain an employee is money and conditions.