Mr. Gruber [yes, it's THAT Jonathan Gruber] found that when retirees in California began visiting their doctor less often and filling fewer prescriptions, overall medical spending fell. People did get sick more often, but treating their illnesses was still less costly than widespread basic care — in the form of doctors visits and drugs. ... As Dr. Mark R. Chassin, a former New York state health commissioner, says, preventive care “reduces costs, yes, for the individual who didn’t get sick.” [1]
You go on to state that the additional productivity of the person we saved also nets us additional savings. But the same article contradicts this notion as well:
The actual savings are also not as large as might at first seem. Even if you don’t develop diabetes, your lifetime medical costs won’t drop to zero. You might live longer and better and yet still ultimately run up almost as big a lifetime medical bill, because you’ll eventually have other problems. That would be an undeniably better outcome, but it wouldn’t produce a financial windfall for society.
You go on to suggest that medical professionals would not be wasting money on doing too many tests: "For any given test and set of circumstances under which it is administered there can be a cost benefit analysis."
That seems logical, but it's not how the real world works. People get emotional about the potential risks, and demand the tests even when there's not a clear indication. You might remember the hubbub a couple of years ago when it was suggested, based on historical evidence, that regular mammograms should be delayed a few years later than was currently the practice. But women's health advocacy groups raised such a hue and cry that the actual medical guidelines were not changed to follow the evidence.
[1] https://www.nytimes.com/2007/08/08/business/08leonhardt.html
Firstly putting a bullet in the head of anyone with non trivial cancer would probably be a financial savings for the insurer but the real equation is the human/societal benefit of treatment vs costs to best make use of a finite resource.
A simple cost of treatment analysis even misses out on the income that a person would have earned had they not died and the money that could have been paid in taxes and used to fund more treatment.
Drilling down into just the cost of treatment your statement isn't even wrong its a category error like saying that adding 2 integers always yields a number greater than 42.
For any given test and set of circumstances under which it is administered there can be a cost benefit analysis.
Example if you spend a thousand dollars on each false positive result and save 10k for each and have a 1% false positive rate and test a million people with a 1 in a million true positive rate. You will find one true positive saving 10k unfortunately you will also find 10k false positives and waste 10 million dollars.
In actuality you wouldn't do this you would test people whose symptoms or circumstances suggest they are likely to have it.
It seems fantastic to suggest that preventative medicine is always financially negative when people who actually study health care say otherwise.