Unless you've killed game, it's hard to have a sense of what it takes to kill something quickly. It's hard. Your shot has to be perfect. Even shots in the head don't necessarily kill large game quickly.
A friend once witnessed someone shoot a bison in the head with a high-powered rifle at 30 yards, and the bison didn't even seem to notice. He shot it in the head again and it fell down, and as they started walking towards it the bison got right back up and charged them, then turned away and jogged about 1.5 miles before settling down to graze. They caught up with it and shot it square in the head again with the same high-powered rifle and it shuddered, looked like it would charge again, but went back to grazing. They shot it in the head a fourth time, and finally this shot took it down. If it's this hard to kill large game with a high-powered rifle, it's all the more challenging to do it with spears, or arrows.
Even when you shoot something with a high-powered rifle, kills are seldom neat and clean. The only reason the ideal of a quick, clean kill is still alive within our society is because most people don't hunt anymore and because the only point of comparison we have is the killing of domestic animals which we rarely see in person. Most kills of domestic animals are far from clean or quick. I've seen pig skulls where it took 2, 3, sometimes even 4 bullets in the brain before the pig actually died. Cows are the same. Some big slaughterhouses don't even try to kill the cows, they just want to immobilize them. So one or two bullets in the brain immobilizes the cow enough to let the workers start skinning it, and the cow is essentially skinned alive, feeling the whole process until it goes unconscious due to shock. It might not actually die until it is gutted.
We treat animals like commodities; they've lost the quality of being alive and are merely products to be bought and sold. While the videos of killing the elephants and hippos may seem brutal by our idealized standards, at least they didn't treat the animals like commodities.