I went to a very interesting debate about 'presumed consent' - ie the opt-out idea. There were three speakers for, and three against - the most outspoken AGAINST opt-out was a transplant recipient, and the most outspoken audience member AGAINST was a chap sitting in front of me, who was again a (far more recent) transplant recipient. I went from thinking of course opt-out was the way to go, to being really unconvinced one way or the other. The argument that got me thinking was that when opt-out has been introduced in other countries, it has only succeeded if there has been MASSIVE publicity around it, and it then becomes impossible to say whether it's the publicity and increased awareness, or the opt-out legislation, that's caused the increase in transplants. In some countries it's gone hugely wrong, and the legislation has been reversed. There was also the fact that the infrastructure to ensure that the right decisions were made (you need to be very VERY sure that someone hasn't opted out before you taken their organs) is huge and complicated, and that ethically you would still need to allow next of kin to veto the decision not to opt-out ... it's far more complicated than I'd realised.
Someone there mentioned the OP's idea of not-on-register, don't-get-organ. None of the panellists agreed. Personally, I thought of a situation where a whole family is not keen on organ donation, no one carries a card, no one on the register - not religious, they all just think it's a bit ick, inasmuch as they think about it at all. Then one of them gets sick, needs a transplant. Scenario 1 - he's not on the register, so he is refused a transplant. He dies the family are retrenched in their views, transplants are bad. Those parts of him which could have been used despite his illness, are not used. Nothing changes. Scenario 2 - he receives a transplant. He gets better. He registers as a donor, although he knows few parts of him will be fit for transplant. The family are so grateful for his recovery that some of them register. One starts giving blood ... something changes.