Now, I appreciate that my circumstances are not directly comparable to that of a police officer responding to an emergency call; however, the basic methodology should be applicable in both cases.
Police officers are granted a monopoly on applying force on the civilian population; with that privilege comes great responsibility to use that privilege sparingly and proportionate to the situation they are sent to resolve.
I do not expect the police to disarm completely - that wouldn't be realistic - but as a member of the public I do expect them to show restraint and train -and aim for- non-lethal outcomes in encounters with the public. They have, after all, taken an oath to serve us. I hardly think the best way of serving is to assume civilians are hostile until proven otherwise.
I have yet to injure myself; in large part I ascribe this to the fact that I always think and think again about what I am about to do, and how it may conceivably put me at risk, then take the required measures to eliminate that risk.
However, more importantly - I have also yet to have anybody else injured on my watch. Why? Because I am not only concerned about my own safety, but also that of anybody who are, or may possibly come, within the blast radius in case something goes pear-shaped.
I would expect police officers to do the same - though granted, most of the time they have to make their decisions much faster (which makes it even more important to think things through beforehand - and, hopefully, come up with alternatives to "Shoot at anything you are not 100% certain is harmless, then sort out the details after the gunsmoke clears."