Maybe market magic would be more efficient, I doubt that in practice it would particularly show up.
I also wonder if cutting the above market clearing compensation would come for free, or if there are real reasons for it.
Edit to add: also, notice that you've addressed something different than what I said; you argue that it could cost less, not that the public would avoid paying.
Here's a law review article that reports the results of a national study on police officer indemnification: http://www.nyulawreview.org/sites/default/files/pdf/NYULawRe...
My study reveals that police officers are virtually always indemnified: During the study period, governments paid approximately 99.98% of the dollars that plaintiffs recovered in lawsuits alleging civil rights violations by law enforcement. Law enforcement officers in my study never satisfied a punitive damages award entered against them and almost never contributed anything to settlements or judgments—even when indemnification was prohibited by law or policy, and even when officers were disciplined, terminated, or prosecuted for their conduct.
In what percentage of cases would you guess that automobile insurance premiums rise where a driver is found liable for an incident and the insurance company is forced to pay out?
So sure, there's a good possibility that requiring police to carry individual liability insurance would lower costs. The public would still ultimately fund the premiums on that insurance.
Second, if officers are forced to seek out indemnification on the open market these policies will be underwritten. Bad risks will be forced off the job through unaffordable policies. Whereas blanket indemnification by the taxpayer has no selection effect at all.