I see your point with people losing trust in doctors. A person might begin to think that the physician is no longer delivering optimum health service because there's someone else who has paid good sum and is in need of a transplant.
The whole rationale behind the donation is understood, but people should make that call for themselves or their families should(if the person is already deceased).
Yes, people should decide for themselves not that the government should decide for them. Also, if people see that doctors are not trying their best to save the patients just because some people are in need of organs they will start losing their trust on them.