Your points about there being a great difference between LEO actions, and a private person, are valid. One runs towards a problem, the other tries to move away, or avoid the problem!
A normal person is not out walking the backstreets, on a dark night, trying to find the mugger, nor traveling to answer a call about a DV, drugged idiot, or to find criminal activity!!
What I did find interesting is the comments of some that, in the USA, a Police officer is not required to go towards gunfire, to protect the public, only to protect a prisoner!
Umm I had never actually considered that NOT responding to an armed offender, or shots fired, was an option for the Police!?
I am not certain how to completely answer this, but yes, a person, who is in police custody, absolutely must be protected. When I took a person into custody, or an impaired person came to be in my care, I took ownership of that person’s safety, until they were delivered to a jail, to a medical facility, or, if applicable, released in a safe environment. To do otherwise could be seen as violating the individual’s civil rights, as guaranteed by the U.S. Constitution.
And, there is a court case, that went all the way to the US Supreme Court, with an ultimate finding that a police department is responsible for the safety of the entire public at large, and not necessarily responsible for the safety of any one member of the public. The case dealt with response to a specific address, for a call for service, but I recall no details. Obviously, this court decision does not abrogate the responsibility to protect the civil rights of a person in custody.
An individual peace officer, in the USA, is not expected to needlessly throw his/her life away, in a vain attempt to stop a dangerous criminal act, but, a failure to act, in a reasonable manner, can result in disciplinary action, and in some jurisdictions, prosecution for neglect of duty. I wore a badge, for the city of Houston, Texas, from 1984 to 2018, and knew that I was expected to go toward the sound of the guns, if at all reasonably possible. Indeed, for much of the Eighties, and perhaps well into the Nineties, I was actually required to be armed at all times, with a handgun of at least .380 ACP or .38 Special power level, and “always subject to duty.”
Eventually, the requirement to be armed, while off the clock, was rescinded, but being “always subject to duty” remained, which was generally interpreted to mean that a reasonable attempt to be a good witness, and get a detailed suspect description, remained a requirement. It was understood that an off-the-clock officer, who was accompanied by family members, should not place his family members in danger, as the officer’s priority to protect his/her family was reasonable.
Our “active shooter” training did emphasize the need to intervene to protect the public, at a mass-homicide event, with survival of self being subordinate to stopping the killing. For the first time, “going home at the end of your shift” was specifically moved to secondary priority, with stopping the killing being given top priority. We were trained to proceed immediately to the killer’s location, preferably in a small team, but, alone, if necessary. If this idea bothered us, we were advised to find another occupation. Part of the active shooter training was an emphasis on carrying duty/service pistols during personal time, though the requirement to be armed 24/7/365 was not re-instituted. (Very few departments/agencies want to require an officer/agent to always carry a weapon, anymore, because, for one reason another, being intoxicated, or impaired by medication, at least on occasion, is part of the human condition.)