That's a good point, Milly's Mum. I suspect that many transplants would be about prolonging the life of already elderly cats, and I would strongly disagree with this. The only possible justification I can see, is for corrective surgery in younger animals, eg. for malformed heart valves / heart murmurs, etc - but then, corrective surgery for minor defects in young animals is of course not the same as organ transplant (though I have heard of heart valve replacements, but these tend to be synthetic, not from donors).
I would add that most animal behaviour experts differentiate between pain and distress - pain is physical discomfort, and as animals do not intellectualise or emotionalise physical pain like humans, they can actually tolerate it better than we can (which is not to say we shouldn't do everything in our power to prevent them experiencing pain), however, animals are less able to cope with distress - traumatising experiences, fear, loss of control, entrapment, persecution, abuse, confinement etc - relative to humans.
We should be very careful about how we evaluate pain or physical discomfort in quality of life - even humans do not rate pain in the same way - many terminal patients would rather experience pain and a clear mind than the frightening disorientation and lack of control caused by some opiates. This clearly illustrates that while discomfort may be associated with distress in some cases, distress is more complex than physical discomfort, and can occur in the absence of pain. Conversley, physical discomfort can occur without causing distress. If this level of complexity is evident in cats, dogs, ferrrets and humans, we must be very cautious about how we assess and interpret "quality of life", both in humans, and in animals.
That being said, I would still be against transplants in older animals, but can, possibly, see the benefit for the correction of congenital problems in young animals.