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> Your argument is sound. It is however, built on one glaring assumption: the people in charge of the publicly funded healthcare systems are primarily incentivized to find cheap and safe treatments for the illness.

In many countries, they do. In some (like Brazil and India), they even rebelled and fought for their right to do so at some point (saving lives of people in other countries by the way).

I mean, in theory, all governments should care, but some are corrupted, and some have been designed to work against the best interests of the patient.