> The trouble with that logic, as the US courts figured out, was that if the police could be held accountable for misdeeds done while allegedly doing their job then so could other public officials, like judges.

That's not trouble, it's a strong selling point. No public official should be immune from accountability for their crimes. Transparency and accountability would solve a lot of problems. Any public official uncomfortable with the idea of not being able to commit crimes and civil rights violations with impunity isn't fit for the job they have.