These are interesting comments; let me reply to a few of them.
One comment suggests plausibly that while some people are reluctant to opt in to organ donation for fear that doctors will be more inclined to pronounce them dead (opting in increases one's value dead!), they would be equally reluctant to opt out because it would identify them as selfish or fearful. Another comment suggests also plausibly that people don't like to think about death and so they will leave blank a question about donating their organs, whatever the question says.
One comment suggests that organ donors be given priority in receipt of organs. That is worth considering as a means of encouraging organ donation, but it has a drawback: people with kidney or lung problems would be quick to sign up as donors! Yet if they died, their organs would not be usable, because diseased, for transplants. So people wanting to sign up as donors would have to be screened before being given the priority; and just the bother of screening would reduce the number of donors, even healthy ones who would sign up if assured of priority.
A physician comments that one problem with a market solution is that it will result in some substitution of the organs of living persons for the organs of cadavers, and the operation poses some risk to the (living) donor and also deprives him of an organ that he may need in the future. So this is an argument for opt in.
Finally, regarding the prohibition of other forms of commodification, such as the gladiatorial contest, one comment sensibly points out that some at least of these prohibitions may have anticompetitive origins: if you would like to be a boxer and think you would be good at it, you might want boxing gloves to be required, lest you lose some or all of your market to fighters less skillful than you but willing to fight each other without gloves.