If someone is in my sights, I assure you that my reaction time would be more than sufficient to differentiate between a man removing a holstered weapon from his belt and a man who was taking that weapon out of that holster. And I’m not a trained LEO.
And the weight in a situation where the man in my sights is in a crowd of innocent bystanders would sway heavily towards not pulling the trigger until I’m positive he is really a threat to anyone.
At a minimum, the cops handled it wrong by approaching the guy in the most crowded spot they could find. The risk to innocent bystanders was huge and not needed.
Also - speed in making the shooting decision isn’t critical. If a man is shot anywhere but the brain or CNS, he can shoot back for 10-20 seconds...long enough to empty most semi-automatics. If you are going to trade shots with a guy, firing your shot .5 seconds before he shoots you means he’ll die a moment before you do -assuming you both hit the target.
If you have set up the arrest so that trading shots toe-to-toe can happen, then you have already accepted your death as a reasonable outcome - assuming the BG is really a Bad Guy and not a shopper with a CCW permit.
One of the faults with most gun training is that they emphasize speed in getting your shot off. In reality, accuracy is far more important, and the extra half second to confirm the threat isn’t going to hurt you much - IF he is a hard case bad guy. Of course, if he is innocent, it helps one kill an innocent man faster...