Earlier quoted context omitted.
A big issue with allowing organ markets is that impoverished people can practically be forced to sell their organs.
Yes, often welfare systems won't give you aid if you have assets such as cash or a home. Would your organs be considered assets?
What I worry about, is in countries like the US/UK where "having a student debt" has somehow become a badge of honour, I can see "selling a kidney" to get through university becoming the same honourable demonstration that you are committed to do what it take to succeed.
... and by extension, show people who are not as committed. You can see it coming: "my son sold his kidney to succeed, why should we give even more to the people that are not even ready to take such a small step".
In general, we seem to expect people to take an ever growing amount of risk for the reward of maintaining their social standing. Being able to sell your body in piece is just raising the bar even higher.