I was shown a police officer early in my job which showed a dead police officer who had the drop on the BG but failed to take the safety off on his HP.
that should have been a teaching point to train with your safety, rather than to take it off too early
IMO, this is something of an AR/M16 specific practice. A mini-14, M1 carbine, Garand, AK, anything with a crossbolt safety, or any handgun with anything other than a 1911-style safety is not very conducive to flicking the safety on and off and on and off as you raise and lower the weapon. And it is my observation that even most 1911 users flick off the safety during the draw and put it back on prior to reholstering , rather than going on and off and on and off while the weapon is in use.
that's just lazy, i could understand it with a slide mounted safety, but there's no excuse with a 1911...it would be like walking around with cocked DA wheelgun.
WTIW: some cross bolt safeties are easier to flick off than others. i can disengage the safety on my FN SLP with the 2nd joint of my index finger...alot like you would a Vang Comp extended safety on a 870