This is an interesting perspective. I think primarily the reason why the police have so many confrontational issues has to do with it being a paramilitary organization. More women officers would offer different perspectives and alternative to deescalate situations, but that would only put a dent in overcoming the "us vs. them" mentality along with the institutionalized discrimination (I mean the L.A. SWAT team was invented for the sole purpose of keeping low income non whites in their neighbourhoods).
More importantly we need women AND men of all different backgrounds on these police forces. Unfortunately the very same people we need more of in the police, more often than not grow up mistrusting and resenting them and want to disassociate with them altogether. We don't invest in crime prevention...rather we profited by creating a system aimed at controlling minorities and are reactive to crime. Until some of our inequalities have be leveled out (unfair first drug offense arrests, racial profiling etc.) we will continue to see those headlines you despise.
You are right though, there are not nearly enough efforts to hire intelligent officers with negotiating skills in addition to physical strength. And honestly, I believe it is because no one in power wants to invest in breaking down the criminal justice systems to even the odds.
I don't have all the answers to solving this problem because it's basically a drug-resistant metastasized cancer on an elephant living near a toxic waste dump-- there's no one reason for the problem and many attempts to cure have not been fruitful.