There is a core difference in these. Two really. Consent and violence. A police doing their job is often acting against your consent and invoking violence. Doctors don't. Well cutting you might be violent, but they are sure to get your consent and it is for your well being, to say nothing of the difference in training requirements before a doctor is allowed to touch you with a scalpel. And then they have to carry malpractice insurance while cops do not have to do similar.
When a police officer arrests you, they are doing something to you that in any other situation would be a major crime and it is not done in your best interest. This significantly changes the reasoning and, especially in light of recent events, needs a significant improvement in how it is currently legally treated.