"For the life of me, I can't figure out why in USA Police officers go immediately to murder &....."

[Lee-Lee]

46. Because the whole premise of that post is based on false assumptions

First, what that post doesn't say about the military ROE is that while all those escalating steps are recommended, they are not mandated and it is ultimately at that person discretion what steps can be safely taken without undo risk- if the situation escalates so quickly that lethal force is needed as the first step that's how it's done.

The second false premise is that cops jump straight to "murder". That's proven false by how many arrests every day, thousands of which the person arrested resists with violence. The escalation of force continuum in a modern policy agency is like the ROE rules mentioned in the above post in that there are many steps, but just like them it's all based on the officers judgement and risk to them and the public. Different agency's have different models but they all are something like this:

Officer presence- just being there fixes the problem.
Soft words- commands given at normal voice and tone
Harsh words- commands given loudly and forcefully.
Empty hands- taking hands on to force compliance
Striking weapons (not always used now and something swapped in position with the next one)- items like a baton or ASP
Less lethal weapons- taser, OC spray, etc
Lethal force

And the officer can move from one step to any others in a matter of seconds depending on the situation- if an officer is using soft voice and a person pulls a knife and runs at them they will jump over all the rest to lethal force and be justified in it, as an example.