Police officers aren't even in the top ten most dangerous professions [1]. They rank far under such notoriously dangerous jobs as "Grounds Maintenance Workers". According to that source, the BLS, "Police officers incurred 51 homicides in 2016". That's not nothing, but let's not blow it out of proportion to push our views.
Additionally, if a police officer can't handle the stress of a potential threat inherent in their job without killing citizens, they're not qualified to do their job. You mentioned being in the Army being a worse threat than being a police officer. How are Army personnel handled when they are involved in an unjustified shooting?
1: Warning PDF https://www.bls.gov/news.release/pdf/cfoi.pdf