There are different protocols that occur in responding to life-threatening situations for LEO. Police/LEO are often first on scene and do have to first assess the situation. If the situation is a downed power line and standing water and people in the water, the LEO is not supposed to wade into that hazard as he/she may be killed by electrocution. Same if a person is drowning in swift water, the officer is not supposed to go in-- it is against the protocol (even though some do it). In that sense, he/she can/should assess as to not create more victims. In the case of car chase, LEO are supposed to assess if civilians could be harmed and work with their superiors to determine a course of action. In this sense, he/she would not just be blowing out tires and ramming the car on the highway without guidance. In the case of a person with a gun who has held up someone and ran into a darkened stairwell, the officer is to proceed with caution and not just shoot in the dimmed stairwell (Peter Lang, NYPD, convicted). The officer has a duty to survey the scene-- to ensure safety of civilians and protection of the LEO.
All that said, in an active shooter scenario, the protocol is to move quickly to neutralize/distract the shooter in any way they can. There is no surveying the scene beyond going in. Everything is rapid movement. This protocol does mean that innocent people may be killed or hurt. This protocol does mean that there is a greater risk of injury or death for those who are moving in on the shooter. That is why LEO would want more than one officer going in but one going in is also supported.
EMS and other first responders, including fire, will always wait until the scene is safe to provide care. It is part of the protocol. He/she is not supposed to create more victims.