I don’t understand how you can ignite market forces in health care. How else can you balance priorities for all the different uses that people’s financial resources can be used for? What does it even mean to let science decide? No cap on spending?
In the case of cancer, it means a patient should be given the appropriate dose for their diagnosis, as determined by what science has shown to be effective.
Typically, QALYs, Quality Adjusted Life Years. We decide how much (in dollar terms if you're just that fundamentalist about it, but person hours or other metrics are fine too) a QALY is worth, and we will spend no more than that on healthcare interventions.
The set of situations where there's a viable intervention but it's too expensive isn't empty, but it's not large either, so, you just build a bureaucracy to handle those cases.
1) on the medical provider end, find every possible excuse to charge 1% more and pay it out to themselves, not using it for patient care
2) on the insurance/government end, find every possible way to charge 1% less, no matter the cost
So yes "let science decide" means to let doctors decide what care to provide (meaning you'd need a difficult admissions test for this class of people). Yes, they will cheat, which will benefit themselves, but also patients. And there's a limit, because doctors are fundamentally limited. And then you just eat the cost, and have a board (IMPORTANT: of doctors) weed out the worst abusers on a regular basis. And yes, if a doctor says "spend X on this patient", then we spend X on that patient. End of discussion.
And yes, this is probably "mercantilist" instead of capitalist, and provides a fundamentally unfair advantage in the economy to people who manage to get the degree of medical doctor. In trade, you get good health care.