Moon, the operative word is "needless"
whether it is human or animal. Needless as in "we're doing stuff without a reasonable expectation of a positive outcome". In your case, throat cancer is pretty resistant to treatment, or more correctly, there is little published evidence of successful approaches. Faced with that, I would do as you did. In the case of localized bone cancer, amputation is considered about 90% curative (the other 10% being metastasis that was too early to detect), and the dogs are amazingly adaptable. Losing a hind leg is slightly better than a foreleg since less weight is carried on the hind end, but either is very common. There is some work being done on constructing prosthetics as well, merging the veterinary field with DoD's massive program of prosthetic research. In order to construct a dog prosthetic, the human prosthetic scientists are forced to reexamine their conventional thinking, and in doing so, have made some interesting advances in human prosthetic design. Intellectually, it is also a morale-booster to watch a dog wearing your prosthetic chase a ball down a hallway.