Professional insurance of the variety that doctors get doesn't cover reckless or malicious behavior. Insurance that covered the things that cops presently ought to be sued for would not be affordable.

What you are describing is another complex layer which would be liable to be perverted to serve establish interests because that is inevitably what happens with complex systems with powerful entrenched interests.

5 years after implementation we would be talking about why it had fixed none of our problems and how we needed to fix it which would be politically as hard as implementing it in the first place with the primary difference between now and then being paying a big bundle of money to the insurance industry. Instead of political pressure to just pay off the people the officers shot there would be political pressure to just subsidize the problem officers insurance payments and then STILL pay out for most of the egregious stuff that isn't covered. Most of the time a "market solution" makes as much sense as the people who faced with a technical problem yell "BLOCKCHAIN!"

Personal liability is still a complex system subject to the same forces but the less it is polluted with cop specific process the more likely that it will actually work because its harder to pervert the entire process of civil litigation than it is to pervert an incestuous insurance market that services the law enforcement industry.