Transplants aren't unrealistic to perform, but clinging to life in that manner is.
If transplants become the norm people will come to expect them, and will have even less appreciation for mortality, therefore be more tied to staying alive as long as possible. There'd be little fear of something like organ failure because the answer will always be to "just get a new one". We then lose a bit more appreciation for death and come closer to expecting immortality, which is what is unrealistic.