Quick tangential question: Do you see a benefit in incoming medical students knowing programming? If so, which specialty do you see it benefiting from the most (e.g., radiology)?
Now, doing anything more than shitty statistics or code-monkey javascript is almost impossible due to other constraints. In medicine, almost every system is totally locked up. There are of course exceptions as some students will go above and beyond, but the yield in terms of work/achievement will always be poor. It's far easier to just fill in excel spreadsheets and publish lots of shitty papers. Much to my dismay.
As for the sibling comment speaking of abstraction I'm sorry to disappoint, but no. Current medicine is far from being hard science. You cannot approach it like a formal system (yet). These days, docs are still far closer to gardeners than they are to programmers or any kind of engineer.
That said, you can find use cases for programming in any specialty. Sometimes it will be more obvious than others:
Image analysis -> radiology
Statistical genomics -> genetics
Dsp -> anesthesia
...
But anyways, don't get your hopes up too much. Students would usually be much better served by learning to care for people. And that doesn't involve programming.