First, there is a reasonably new program in some medical schools to specifically admit students whose undergraduate training was in the humanities, not the physical sciences.
Second, we (society and medical professionals, more specifically) have no idea how to treat and care for end-of-life patients. (Warning: this article is horribly sad.)
I am in no position to offer further thoughts on this matter at present besides the following: I still don't know whether offering medical classes to non-medical doctors would ultimately be good for everybody. Nor do I know if I care, when I go to the doctor, how broadly read in the humanities he is. But I do know that there is a reason medicine is still fundamentally practiced by humans, not robots.
