This is more a culinary and ethical argument than efficiency or safety. One should use the whole animal, in all its varieties, because they're delicious. Grinding otherwise edible parts of an animal killed on one's behalf because one disfavors (or is repulsed by) them seems to me much worse than the killing. Eat - and enjoy! - all of it or don't kill it.
It’s definitely better to freeze the left over bits and grind it yourself, but half the animal gets ground up regardless.
Who are you to say that it's wrong for me to enjoy some parts of the animal ground up, versus in their original shape? Either way the entire animal is being eaten and enjoyed, so there's no reasonable moral basis on which to say it's wrong. Your position would make sense if people were throwing away the cheek, tongue, etc but we aren't.