No, we don't. For comparison, in Germany, a slightly larger country, where officers are armed, less than one officer per year died in the past decade:
https://www.dw.com/en/two-german-police-officers-killed-by-f...
If officers don't engage because they are insufficiently equipped, you effectively have less policing. Less policing causes more violence and more deaths.
"Stop and frisk" works:
https://www.npr.org/2012/05/15/152764402/stop-and-frisk-work...
Knife crime in the UK keeps going up...
https://www.bbc.com/news/uk-42749089
...as a result of literally defunding the police:
https://www.theguardian.com/uk-news/2019/may/02/criminals-go...