"Without that terrifying two-headed dog, in other words, we’d all go down with our failing kidneys."
Eventually we would have found other ways to collect the data needed for safe organ transplants than using live mammals. It probably would have delayed the introduction of transplant procedures on humans, so in that sense there would have been "people going down with failing kidneys" -- but how much suffering can you justify by saying that it might save human lives down the road?
I'm reminded of Kazuo Ishiguro's excellent novel Never Let Me Go.
(--- Major spoiler alert! ---)
It takes place in a sort of parallel-universe Britain of the '70s and '80s where human cloning was invented just after WWII. Cloning has become the cure for cancer: just grow a steady supply of live clones, take their organs and transplant them to cancer-inflicted patients.... Of course it takes about 18 years to grow a clone, and you can't just keep these people in a vat somewhere. So the clones are people without citizen rights, whose sole mission in life is to be harvested eventually. Society sees this as justified because clones are not "real people" anyway -- and more importantly, nobody wants to turn the clock back to an era when people regularly died of cancer.