I'm curious to learn how/why you think "the treatment of Western children with life-threatening illnesses is arguably the single most overfunded branch of the medical profession."
As a matter of dollars-spent (total or per-patient), I'd suggest that the money spent on Western adults is far greater and to no surprise. Last I read, children represent 50% of the lives on Medicaid, for example, yet make up only 5% of the inpatient dollars spent. Not proof, I realize, but telling.
Further, I'd consider money spent on children a potential investment while the money spent on dying adults to be potentially wasteful.