Not being protected from prosecution doesn't stop cops from engaging in self defense. If you genuinely think you are in danger as a cop you are willing to break the law to survive and accept being fired as a consequence. Protection from prosecution means there is no consequence to "premature self defense". If a citizen is perceived to possess a weapon but does not draw or fire it the cop still has an alibi that can be used to justify pulling the trigger.

I have seen a video where four cops randomly shot a man with a tazer. That man had no intention of escaping. The excessive use of police force served no purpose. It didn't make the job safer.