I think the elasticity of the demand depends pretty heavily upon the urgency of the problem.

And the demand - as you pointed out - also depends heavily on trust. That said, most health problems aren't unique enough to require a completely bespoke solution.

So at least hypothetically, it's possible to shop around IF pricing and other data were available. But they are not, at least generally.

I found this book rather interesting -- https://www.amazon.com/dp/B01DRXKWRM/ref=dp-kindle-redirect?... -- where a company compiled their health care expenditures and made the data available to their employees.