Doctors and nurses are not required, and in many instances do not have, personal malpractice liability insurance.
Nurses, in particular, tend to be employed by companies which carry policies covering those companies and their agents. There is typically nothing to be gained by suing a $40 an hour nurse for malpractice. You sue the hospital which employed the nurse. The nurse is a party to that suit simply as agent for the hospital.
The same is true of police claims. You aren't going to find a lawyer who, on contingency, is going to sue some cop with little or no savings and maybe some equity in a house or other property. What would be the point?
Finally, in most instances, governments are already carrying liability insurance to cover the actions of their employees, whether they are police or not. But police department insurance is a normal insurance product:
https://www.travelers.com/business-insurance/general-liability/law-enforcement
Law enforcement liability insurance provides coverage for bodily injury, personal injury or property damage caused by a wrongful act committed by or on behalf of a public entity while conducting law enforcement activities or operations.
Even if you had some requirement that individual police officers carry liability insurance, they are still all working for the police department in the course of their duties and the police department, as principal, remains liable for the actions of its agents.