This is the reality. When we eat meat, it's because an animal has died.
I hate cruelty to animals so I either eat vegan or buy pastured, grass fed meat, eggs, etc. Because factory farms are cruel. But a quick slaughter as you describe does not bother me. As long as the knife is super sharp, the animal probably barely feels the pain.
When I eat out at restaurants I eat vegan unless I go to one of the rare places that do serve pastured eggs and meat. Because I am on a budget, even when I cook, I eat vegan about half the time. But that's probably keeping me healthier as well as allowing me to not add to the torture of animals.