As a personal believe, I think it´s inmoral to develope an organ market since the offering would definetly be composed in a great part by low income people and people who want to satisfy empty material desires such as a trip to Las Vegas or a new car.
If we monetize and accept the formation of an organ market, it is accepting that the system has failed in providing everyone the means to get what they need, and instead of building better policy in order to achieve that, we are practicly accepting human mutilation as a relieve for that matter.
Now, one thing is what we beleive, and other thing is what is truly happening. We live on a context where human organ trafficking is a reality, and a tough one to reverse, where donners are way far from having the proper care when giving their organs, and also receiving less than half of the final price of their organs. Here, a well regulated market could make that those people receive the proper caring and at least get way more for their organs, which really is a great sacrifice.
Although that could give some relieve to that matter, regulation would need to take care of other distortions like:
The introduction and “acceptance” of the organ market could lead to an excessive incremet of offer, which could make prices go beyond actual prices, making it even worse for those who are already selling their organs, and definetly deteriorating human life value.
The introduction of the market could disincentivize organ donation, making that people who need an organ and can’t afford it, find it impossible to get it.
By all this, I think that an organ market could relieve (but not fix) some problems for the most vulnerable people but, without proper regulation, it could magnify other society problems.
In that way, I think that a properly stablished exchange market seems way more proper, just as Esteban apointed.
I found an article written by the president of a social justice organization who desinterestedly donated a kidney. He gives some ideas on how a regulated organ market could relieve some society problems. I leave the link for anybody who could be interested.