Visit arid Africa: eating an animal before it was /used properly/ (could be as simple as fertilizing the land here in southern Morocco) is considered wasteful.
I wouldn't know about Africa. But I know a thing or two about keeping animals at the edge of the arctic.
If you butcher when the animals are old, you have quite a bit lower risk of losing the meat due to disease, because old animals fall ill more than young ones.
If you butcher, you have some control over the timing, which helps with using the food. You don't have perfect control, but more than random, and you reduce the risk of having to throw anything away.
So if you use the animals both live and dead, it makes sense to optimise for keeping them alive long and die while still healthy (healthy enough to eat/use, if you want to be cynic).
Does my car stop working because its old? Strictly speaking no, there will be a cause of failure, in practice everything wears out, age has increased the chances of things wearing out, so after a certain point age becomes a 'good enough' reason.
I suppose if you want to be pedantic, a common failure mode isn't actually 'correct'. A heart attack isn't the cause of death, its oxygen starvation, so I'm not sure more 'correct' equals more useful.