Or an extra level of danger if you find yourself in a life-or-death situation, with adrenaline pumping through your veins, your mind tunnelled down on the threat, your fine motor control shot to hell, and you thereby forget that you have to click the safety off. I gather there've been some cops who were killed in shootouts found to have a full magazine and a round in the chamber, but the safety on.
If the perp takes your gun away, odds are you either drew it too late, waited too long to shoot, or weren't mentally prepared and serious about shooting in the first place and telegraphed that to the perp. That is, unless you're a cop who's forced to carry openly out where they can grab it.
As for "loser perps" - it's a mistake to underestimate them. They don't have anything to do all day in prison except work out and practice disarming techniques on each other.
That's why in the quick access safe I don't leave it on, but in the holster I've trained (hundreds of hours) to drop the safety just after I pull the pistol clear of the holster.
Consider this a free plug for Front Sight Firearms Training Institute. They can take a newbie and turn them into an excellent handler in 4 days.
Cops wouldn't need level III holsters if they weren't all switching to Glocks that don't have a thumb safety. It's not natural to grab a pistol with your thumb in the postition necessarry to drop the thumb safety which is why cops have been saved by having one after a perp takes the weapon. You have to train yourself to drop the thumb safety. Your correct about the adrenaline screwing with your motor skills but if you train for it you will be fine.