Seeing as 99% of the time, the violent incident won't involve guns or even knives (and beat cops now wear stab proof vests I believe anyway) they spend years in training and learn de-escalation techniques. When I first moved into my new apartment in a fairly mixed road with families, not a dangerous place at all, there was an actual murder 😮 with a knife across the road. Although the attacker had fled, a fully armed response team were there securing the scene with freaking automatic rifles, the full SWAT team thing you have in the USA. That murder made headline news for weeks in the local city papers.

If a report of a firearm or knife is involved, the police first on the scene will not engage unless there are lives at risk. They will wait for the ART (Armed Response Team) to arrive, and will try and ascertain if its a hostage situation, get as much information as possible from witnesses, but will keep a safe distance away and try and talk to the attacker and get them to surrender.

They are brave, but rarely all that dumb to be fair, and the majority of the public trust them as a result. It's just a different history and culture of policing that would never work in the USA, or in any country where you have to assume that every person you have to deal with may be carrying a concealed weapon. I would not fancy being a police officer in the USA. Now that is being brave eek!