I don't think it to be a waste to cull and dispose of the body of a bird that suffers from an untreatable/spreading infection.
On the contrary: For me it would be the sensible thing to do, as I would not even consider to feed such a bird to my dogs.
I don't ever eat a bird that is not totally healthy, and I only ever eat my own birds, as I want to know exactly how they have been raised and fed etc.
https://www.merckvetmanual.com/poultry/trichomonosis/trichomonosis