Hiring, promotion, and firing in a police department is merit- and seniority-based. Neither the police commissioner nor the chief of police have the authority to dismiss any, let alone all, officers without good cause shown. Further, senior officers (sergeants, lieutenants, captains, etc.) have length-of-service requirements that must be met in order to qualify for the position.
Nora Clavicle's appointment of Mrs. Linseed as chief of police is a clear example of quid pro quo, establishing a prima facie case of influence peddling. Both could be dismissed, and Mayor Linseed could be impeached, for corruption, and all three could potentially be subject to criminal charges.
No individual, regardless of their position, can take out an insurance policy on an entire city. Even the city itself could not insure privately-owned properties, only city-owned property.
Batgirl has held her own against multiple trained fighters, but yet she's utterly helpless when Nora Clavicle, with no training whatsoever, grabs her.