Vicki Gregg is stated to be a former LAPD officer that became an FBI agent and novelist. As such, she would not be reinstated into the LAPD to assume command of a unit. At best, she would be used as a consultant or serve on a task force. As a non-LAPD employee, she would have no supervisory authority over the LAPD personnel. In actuality, the LAPD would temporarily assign another Lieutenant to supervise the unit while Beth was out.
Professional female detectives do not wear stiletto heels to work. LAPD dress code for sworn employees requires them to dress in professional attire. Likewise, the LAPD does not allow females to wear bright colored nail polish.