> many people have a quasi-religious belief in the capability of modern medicine to perform what would otherwise be called a miracle. This belief is typically held without any evidence whatsoever.

The thing is, application of the germ theory of disease and Harvey's theory of circulation of the blood by action of the heart (and consequent developed understanding of the role of the blood, and of blood types) did produce miracles. Reliably safe milk and meat. Penicillin. Reliably useful blood transfusions. The tetanus vaccine. The polio vaccine.

The great polio epidemic was only four-ish generations ago. In my childhood I knew one or two people in iron lungs, having contracted polio before the vaccine. The vaccine was miraculous to every parent at the time.

The evidence has been culturally transmitted through the generations.