Earlier quoted context omitted.
This is an interesting thought. Like other professions which have license to affect an individual physically, such as doctors, perhaps the first responders should carry some type of "malpractice" malpractice insurance.
It's turtles all the way down though. If police need to carry malpractice insurance then the cost will have to be built into salary which is paid by the taxpayers. It might be cheaper to just have the state pay out then pay for a bunch of individual insurance policies.
When the state pays directly, there is no incentive for the individual to behave. If the state paid the officer's salary plus a standard 'allowance' equal to the cost of police malpractice insurance for an officer with no claims, then the incentive is to keep their record clean or pay higher rates out of pocket for misbehaviour.