The first time I showed up at formal handgun training that was worth something was with a Beretta 92 Elite I, a G variant. When doing a stress course I de-cocked between every shooting position to move from one place to the other. Some wondered why I did that. I figured that moving around a gravel-covered obstacle course with a cocked handgun wasn't wise.
In the same class was a LE officer who was issued a DAO Sig semi-auto. She ran the same course, but tripped and fell. I distinctly remember seeing the gun jerk in her hand as she grasped it (including with his trigger finger on the trigger) out of sympathetic response. And, of course, the muzzle was not pointed in a safe direction. I could tell because I was actually looking down the barrel when this happened. I'm about 95% sure I was spared from a bullet wound by the length and weight of that Sig's trigger. Not long after that I watched someone narrowly miss their own foot trying to draw their 1911 under the mild stress of an audience and a timer.
When I did more advanced stuff with people who had considerable experience on the gunfighting side, decocking or using the safety of a weapon when moving (1911 or an AR, etc) was emphasized heavily.
Like Todd, when I was running a 1911 my safety was re-engaged anytime I was not actively on the trigger shooting. If the gun came down out of eye line the safety was re-applied. When doing basic room clearing some folks on the catwalk commented on the frequent, audible clicking of my 1911's safety as being unusual.