IMO....If I did save the broth from giblets, I would use it only for mixing with my dog's food. There was a time that I ate giblets (due to the fact that our mother prepared them for us). We actually loved chicken livers. Then, as an adult I became more aware of diet, healthy foods and foods to avoid. Animal organs of any kind are a very bad idea........for numerous logical reasons. In fact, after educating myself, I was disgusted by the fact that we used to eat a lot of things that pose problems. Someone once said to me, "Think about the 'purpose' of a LIVER......it's a filter organ, that traps toxins and poisons." OK......yuk.....how about losing your appetite at the thought?! An animal's body can tolerate this obviously since their system dates back to the "Wild.".......but, would you keep the broth for any other purpose? I wouldn't.
LOL..I know what you mean, Susan. I used to love calves liver, as well as chicken livers. I miss them, but since realizing the facts to what I was eating, I just don't. In fact, 10 yrs ago, I cut ALL red meat out of my diet...various reasons.
If you like the flavor, by all means use it. When I roast a chicken I always save the bones and trimmings (except fat) in the freezer,and when I have a few carcasses I make a stock. Also save and add any vegetable trimmings. After I get all the flavor out I strain itandsimmer it down to make my own chicken base. SO much better than bouillon cubes or canned stock and so much flavor that most people throw away.