It sounds like your perspective is formed form viewing the TV show "Cops". This is not representative of reality.
106 police officers died while on duty in 2018 (of all causes, not just violence from public - 55 officers were feloniously killed while 51 died accidentally). 986 citizens were fatally shot by police in the same year.
Situations where police are able to survive only because they were able to quickdraw and shoot a criminal first like some sort of cowboy are vanishingly rare and possibly purely fantasy. Is trading the lives of a few hundred citizens worth saving the 0-2 cops in these rare situations per year?
Call in the cavalry when needed, but most cops do not need to be armed all the time.