There's a lot of stuff involving patient secrecy that would be convenient to not worry about. Conglomerating everyone's medical records could result in dramatic gains in knowledge on efficacy of treatment. But it should be possible to do that in a way that respects patient secrecy, and I don't think ethics is the true rejection there.

There are a number of cases where people consider it unethical to use controls. AZT is a famous example, where they stopped the study midway through because AZT was so effective for the experimental group, but then some nasty side effects started showing up- and it was unclear how much was due to the AZT, because there wasn't a control group to compare to anymore.

(Assuming that not only institutional ethics but my own sense of morality is not a constraint.)

A lot of the really interesting things we know about broad-scale human neurology, particularly some tricky stuff about the nature of consiousness, are due to the study of people who have suffered brain damage. If there were no ethical constraints, I would deliberately induce carefully controlled forms of brain damage on humans and observe the results.

I am not a doctor. And I have no clue on the methodology they have available avoid ethic trouble. But I can imagine a few things.