May I ask whether you have you ever owned a dog? ;)
I can't think of any quicker and overall safer means of sedation than simply shooting it in the head. It's sad that a dog has to die, but compared to the mess an angry dog can make, its life is simply not worth much.
Not that I really want to sound like I'm defending the policepeople in question here, because that dog shouldn't have died - but it shouldn't have died because there shouldn't have been a situation where they needed to shoot it, not because shooting an attacking dog is the wrong thing to do.
(Yes, I have had a dog. I loved it very much, and it seemed to return the favour. But you have to be clear-eyed about these things.)
A dart gun is useless for stopping animals that are attacking. That's why there is always someone with a shotgun ready to kill the animal that's being darted.
BUT... Every officer near where I live carries a nightclub/billy stick/baton etc. I've been in situation with aggressive dogs out in the country and often a simple kick is enough to back them off... Discharging a firearm at a fast moving animal is reckless and begging for a bystander to be injured.
I love dogs, I've lived with several (medium and large), but you don't mess around with something like that if it decides to get dangerous.
This is the same reason that cops are trained to shoot center-mass and until the attacker is down; this officer responded quickly under stress and safely dispatched his attacker, preventing possible serious injury to both himself and his partner.
If you want to argue that the cops shouldn't have cuffed the guy, I'd absolutely agree. A polite "Now, son, why were you phoning at us?" would've avoided all this nonsense. I can't in clear conscience disagree with the self-defense the officer used.
Also animal control traps or nets the animal before attempting to sedate it. You can't just stick the needle anywhere.