But I do think you should have to 'opt out' with a reasonable excuse rather than expressing your interest onto the register by carrying a card. That in itself would save even more lives, and I'm all for saving lives.
Read Larry Niven's Known Space sci-fi stories.
Someone in the future has the idea that harvesting organs from dead criminals is a good way to save more lives. Great, but there are still too many people needing too few available organs, so then they go from the Death Penalty for Murder in the First Degree to murder in the second degree, kidnapping, manslaughter... until the demand for organs means you can get the death penalty for false advertising or too many speeding tickets.
Since about 1984, China had been harvesting organs from executed prisoners and denying it. Then they finally admitted it and now they are phasing it out see
http://www.bbc.co.uk/news/world-asia-china-23722796So, yes, saving lives may be a good thing, but not when the State starts deciding what happens to your remains.