I thought all (well most) places were "armed" in the US, with all of it's citizens insisting on having guns (including lunatics like this guy)
I don't know where you got that information, but it is wrong.
The wild west is gone. Very few public places or work places have armed security.
As for the Orlando shooter, he was confronted by an armed security guard (off duty police officer) shots were exchanged but neither were hit and the shooter then entered the club.
My concern is that a trained police officer was not accurate with his gun.
Why? This question should be answered. Why did he miss?
Just because police are present does not guarantee this will not happen again.