Then taxpayers would pick up the bill for the higher salary demands of officers due to the cost of insurance, and then the police unions would lobby for targeted tort reform to limit their liability and insurance costs on the basis that it would save the taxpayers money, and succeed, and the structural problems that foster abuse would manage not to be dealt with at all, and the victims even worse off. That's what.
“Let’s absolve ourselves of liability”—which is what this amounts to unless it's a cop proposing it—is just an excuse to avoid addressing the problem.
(Doctor’s malpractice insurance is not instead of their private or public employer being liable as usual under principles like respondeat superior or just plain direct liability for acts aligned with bad policy or direction, and only covers professional negligence, not criminal acts. Mere police malpractice, is—while also an issue, to be sure—not the focus of concern here, and the acts involved are the kind for which it is generally illegal to insure liability for, for good reasons. Insurance for liability incurred through murder is not a thing, and I don't think anyone who has thought it through wants it to be a thing. Except maybe prospective murderers.)