Partial, and originally just an extended comment because I had not seen the scenes and was not in a position to look it up, however:
why do the cops not shoot the suspect's hand to make him drop the gun?
That is a movie myth, like that of the old Western lawman shooting the gun out of a bad guy's hand. Perpetuated by television and movies forever and believed by so many. It is a fantasy.
In real life, Law Enforcement are not trained to shoot to kill, but to shoot to stop the aggressor, so training is for aiming at the “center mass” – the middle of the largest exposed area on the aggressor – because aiming there increases the likelihood of hitting and stopping the aggressor.
I haven't seen these scenes but maybe the writers were trying not to continue that old nonsense.
When it comes to dealing with the use of deadly force, the following applies:
Whenever the actions of the suspect are of such a nature as to create an honest belief in the mind of the officer that he is in danger of death or great bodily harm he is justified in the use of deadly force in self defense.
There are two requirements for the exercise of this privilege:
- that the circumstances be such as to reasonably warrant the belief that the officer's life is threatened, and
- that he honestly believes that such danger exists.
In both of your examples the suspect is not a threat until they are a threat... and deadly force is required. Itty bitty force doesn't exist.
So, the answers to your questions is a combination of all three that you list...
Having said that:
But of course, it is not always black and white, and yes, there have been times that appropriate (and also inappropriate) force has been used that was not quite in the rule book:
https://www.pbs.org/wgbh/frontline/article/shooting-not-to-kill-debate-frustrates-police/
raises the question — one many civilians, including President Joe Biden, have wondered about — why don’t officers, if possible, shoot a suspect there, instead of in the chest or head?
It’s a question that frustrates and annoys many in law enforcement.
Salt Lake City Police Deputy Chief Scott Mourtgos said the expectation an officer could consistently hit these “precision shots” at someone’s leg or arm is “unrealistic” and could put officers and the public in danger when an officer misses.
How officers are trained
At every police academy former officer Randy Shrewsberry has attended, an officer-in-training brings up the question: Why not shoot someone in the leg?
“And the answer is always, ‘Well, have you eliminated the threat if you shoot someone in the leg or the arm?’” said Shrewsberry, who is now the executive director of the California-based Institute for Criminal Justice Training Reform. “‘Do they still have the ability to shoot you?’”
Cadets throughout the nation learn to aim for a person’s torso above the waist, known as one’s center-mass. It’s the biggest part of the body and can’t be moved as quickly out of an officer’s line of fire, like an arm or a leg could. It’s also where humans carry most of their vital organs. So, the logic goes, if officers perceive an imminent threat, their best chance of eliminating that threat quickly is to shoot someone there.
Mourtgos, with Salt Lake City police, said you also can’t expect an officer in a dynamic and stressful situation to consistently hit a small, and sometimes moving, target on a person’s body.
Then, he said, you have to consider a general principle all officers are taught: action is faster than reaction.
If an officer tried to, for instance, shoot a knife out of someone’s hand, Mourtgos said that person could move their hand faster than an officer could perceive it and reassess their aim. If an officer misses, the threat he or she sought to eliminate remains — and the misplaced bullet could hit someone in the background.
And, he said, even when you shoot someone in a part of the body with fewer vital organs, there’s still a possibility the person bleeds to death.
“I’ve seen people survive being shot in the head with a bullet … I’ve seen people die from being shot in the leg and arm,” Mourtgos said. “There is no good place to shoot a human being.”
From the same incident in the article above, a less-than-lethal force was applied, that of the Taser:
Video shows (Officer) Dunn with his pistol in one hand as he aimed his Taser at the woman (Casimiro), who paced slowly, with the other. He fired the Taser twice. The woman had no big reaction, she just said it didn’t work and pulled at the wires.
“Didn’t work, did it?” he responded. “OK, that’s all I got for Taser.”
Casimiro moved slightly, as if to take a step forward. (Officer) Dunn let out a breath and fired his gun at her knee as (Officer) Berg yelled for her to drop the screwdriver.
(Officer Dunn) said he was concerned about the people behind them at the gas station. >If she ran at them, he’d have to fire at her and, if he missed, bullets might hit bystanders.
He added, if that happened, “Then I don’t have the time to aim and make a precise shot that’s not going to kill her. I’m going to hit her center-mass, and it’s going to be a lot of rounds and I’m not going to be able to save her. She’s going to die.”
Shooting not to kill
Law enforcement experts said for a shoot-to-incapacitate policy to work, police would need the following:
- A stable target.
- Good visibility.
- A clear backdrop.
- A skilled shooter.
Most officers don’t shoot at all in their careers, and most officers, when they do shoot, don’t do so under any of these (ideal) conditions, much less all four.
https://www.deseret.com/2015/1/15/20556511/why-police-don-t-aim-for-the-legs
Shooting someone in the leg doesn’t mean he or she will stop shooting.
The same is true of someone who is shot in the arm or shoulder, or even in the chest. Shooting someone in the leg won’t necessarily stop him or her from standing, walking or even running. Shooting someone in the leg doesn’t even mean he or she will fall to the ground. And, it doesn’t mean the individual will stop feloniously aiming a gun at a police officer or an innocent citizen and pulling the trigger.
Even so, if an officer did shoot someone in the leg, there is a chance it could sever the femoral artery and still potentially end that person’s life.
Officers learn how difficult it is to shoot accurately under stress.
An officer can be a near-perfect shooter on the range, but the stress of a real firefight is totally different. Shooting a gun out of a person’s hand is nearly impossible, and it would be dangerous to attempt in real life.
Research by Dr. Bill Lewsinski of the Force Science Research Center shows that during actual officer-involved shooting incidents, officers only accurately hit moving threats 14 percent of the time at distance under 10 feet. On the corollary, attackers successfully hit officers 68 percent of the time within the same distance.
Police are trained to stop the threat.
Police don’t shoot to wound or shoot to kill; they shoot to stop the threat, period. This is not just a manner of semantics either. The moment the threat no longer exists — when a violent criminal stops shooting or drops a weapon, for example — officers stop shooting.
To reiterate, officers are not trained to shoot to kill. Instead they are taught to shoot until the threat has ended.
It is a myth to believe that a single shot from a handgun will stop someone.
Police are taught to keep shooting until the threat stops. Traditionally, officers will shoot twice and assess. Some of this is because of ingrained range training, but for their safety and the safety of others, officers should keep shooting until the threat stops. Just because a person is shot once or twice, if an officer can even tell the person was hit, it doesn’t mean that person is incapacitated or no longer a threat.
(Note: above article is by a serving LE Officer and military veteran)
https://tvtropes.org/pmwiki/pmwiki.php/Main/BlastingItOutOfTheirHands
TV Trope: Blasting It Out of Their Hands
A character shoots a weapon out of another's hand, or shoots their hand in order to force them to drop the weapon.
(Note, yes, I have seen the videos of LE doing just that, but it is pretty rare)
The physiology of why one single shot from police is not enough when use of lethal force is legally justified:
- Unless an airway or certain parts of the central nervous system, such as the brain stem or upper spinal cord, are struck by a bullet, a person isn't guaranteed to lose consciousness until they lose about 40-to-50 percent of their blood.
https://www.nola.com/news/crime_police/article_ae82835c-0212-5e50-a175-85601a1ed8bb.html
During the 4-second video, he said, a total 37 rounds were fired. Huber said in a use-of-force situation, several shots are fired to cause enough damage to stop the person, and also because many of the gunshots generally miss the target.
To demonstrate how quickly shots are fired in use-of-force situations, Huber showed reporters a video of three agents who were instructed to fire their handguns at a target at a fast pace.
Scharf also said it's important to note many shots fired by police miss the target. Avery said officers are generally trained to shoot people from a distance of 6-to-8 feet, so the chances of hitting the target are not high if the distance between the officer and subject extends farther.
Avery said a more critical factor than the number of total shots fired when evaluating proper use of force is the number of bursts. For example, some guns fire a handful of shots in quick succession before there's a lapse in time.
"If we're talking about four-or-five shots in a single burst, it is not that unusual," Avery said.
https://www.ctvnews.ca/world/why-police-shoot-so-many-times-to-bring-down-a-suspect-1.5079592?cache=yes%3Fclipid%3D89750%3Fclipid%3D89619
MULTIPLE OFFICERS OFTEN SHOOT AT ONCE
High shot counts may be attributed to a phenomenon called "sympathetic fire" or "reflexive fire," which occurs when one officer fires on a suspect, so one or more officers with them start firing, too, even if they haven't immediately perceived the suspect to be a threat, Stoughton said.
This can create confusion among the officers, though, he said: They may mistake another officer's shots for the suspect firing shots at them, which could cause them to continue to shoot needlessly.
https://www.npr.org/2022/07/04/1109648170/akron-police-use-of-force
Many officers today are armed with semiautomatic weapons that are able to discharge an entire magazine — usually about 15 or 17 rounds — within seconds, said Obayashi, who also works as a use-of-force consultant to law enforcement agencies.
That means an unwarranted number of bullets may be fired in quick succession by the time an officer realizes it's time to stop firing, he said.
"It's going to take another period of time for your vision to then transmit a signal to the brain saying, 'Oh, OK, the threat is over. I'm going to stop firing.'"
The physiological response cannot be understated, said Maria "Maki" Haberfeld, a professor of police science at John Jay College of Criminal Justice.
"Unfortunately, the adrenaline, the stress, they take over and it cannot be just clinically explained in terms of what's right and what's wrong," she said.
One of the physiological effects of the stress is the inability to see properly, she said.
"Peripheral vision is impaired up to 70%," she said, "which basically impacts the perception of how many bullets actually hit the suspect. So they really don't know if they hit the target."
Add multiple officers to the fold, and the number of bullets discharged increases exponentially.
Historical guideline:
A 1985 ruling by the U.S. Supreme Court set guidelines for when deadly police force is justified, said Peter Scharf, a criminologist with the LSU School of Public Health who authored "Badge and the bullet: Police Use of Deadly Force." Officers can legally shoot to kill or use other deadly force only when the subject of force presents imminent danger of death or serious injury to the officer or others, according to those guidelines.
Prior to the 1985 ruling, Scharf said, officers had more broad discretion to use deadly force. For example, they could shoot a robber running away with a TV set. Now, he said, officers "cannot shoot just so (offenders) won't escape."
