Very often the grimmer the better, in my world. I eat a lot of fillet steaks but that's because I like to eat my beef raw. Besides that, the grimmest parts of the animal are almost always the most nutritiously diverse. Loads of fat, gristle and collagenous tissue. I sucked the gubbins from a chicken's spine the last time I boiled one into a soup. Marvellous! Liver, kidney, heart etc. can be used to resuscitate the dead.
Anyone who doesn't want all the "grim" bits of the animal, just pile 'em up outside my front door. Nose-to-tail "for the win"as the kids say these days. Scrummy yummy in my tummy