They should put a higher priority on "don't kill an innocent person" than on "immediately eliminate anything that could be a threat". Police officers should be trained based on the principle that the loss of an officer's life, while awful, is still less of a tragedy than the death of someone who could be an innocent bystander. They should be trained that when confronting a suspect, an outcome in which the officer and the suspect are both badly injured but alive is better than an outcome where the officer is unharmed and the suspect is dead. It should not be the role of police officers to kill anyone unless that person is unambiguously attempting violence or is planning imminent violence and cannot be deterred in any other way.
So applied to this case, the police officers should not have shot the suspect until they unambiguously saw a gun in his hand. Does that mean that they would be running the risk that the suspect had been faking his sobbing terror and his panicked, confused attempts at immediate compliance for the past three minutes, and that he had in fact decided to pull out a handgun to attack an entire team of police officers who had rifles aimed at his head? Yes, it does mean that they would be running that risk. By waiting until they could clearly see a gun in his hand, there would indeed be a chance that a suspect irrational and suicidal enough to try that could get off one or two hastily aimed shots in the general direction of the officers before being killed by their overwhelmingly superior firepower. But in the actual situation, and I suspect in a great many similar situations, an unnecessary death would have been avoided.
So applied to this case, the police officers should not have shot the suspect until they unambiguously saw a gun in his hand. Does that mean that they would be running the risk that the suspect had been faking his sobbing terror and his panicked, confused attempts at immediate compliance for the past three minutes, and that he had in fact decided to pull out a handgun to attack an entire team of police officers who had rifles aimed at his head? Yes, it does mean that they would be running that risk. By waiting until they could clearly see a gun in his hand, there would indeed be a chance that a suspect irrational and suicidal enough to try that could get off one or two hastily aimed shots in the general direction of the officers before being killed by their overwhelmingly superior firepower. But in the actual situation, and I suspect in a great many similar situations, an unnecessary death would have been avoided.