In almost all cases (I qualify that because I don't know EVERYTHING), medical first responders are not allowed to go in a scene until it has been cleared and made safe by police. The reason for this is to protect those people that can save the lives of the injured.
Think about how many people could be saved by one EMT. If that EMT is taken out, how many people may die?
I think if someone researched this, you would find that this (first responders wait for police clearance) is almost a nationwide policy.
http://www.foxnews.com/us/2018/02/26/florida-emergency-medical-teams-frustrated-over-delay-in-parkland-school-shooting-response.html How long after the 911 calls came in did the first responders arrive? Let's say 10 minutes to arrive and get the equipment out and ready to respond. If they weren't allowed in, as some reported, for up to an hour then that was around the time Cruz was arrested while eating a burger a couple miles away. At Sandy Hook, the cops had the school "cleared", including the roof, in five minutes.
You may very well be (and probably are) correct, but consider the irony of the fact that EMTs were ready, willing and able to charge in to render aid - as combat medics do, but were prevented from doing so by police officers who remained outside.