To simplify the matter for the sake of argument, let's say that there is a child that is certain to die shortly were it not for a magical machine we invented that is guaranteed to save him. However, the machine will only work if we stuff into it half of the world's food supply (it's magical; it can handle it). We wouldn't be willing to pay the price, which in this case would lead to billions of deaths. Even though we had the ability to save a life, we would choose not to.
How does this apply to real life? These types of decisions are made every day by the F.D.A. and other medical standards boards. Poor risk/benefit ratios cause the premature demise of thousands of would-be miracle drugs every year and many already approved procedures can not be performed as ubiquitously as would be most beneficial due to the high costs involved. Would a nationally mandated annual PET scan significantly improve cancer detection rates, and save millions of lives? Yes. But the cost isn't worth the benefit. The machinery is extraordinarily expensive, the radiation would actually cause cancer in a very small subset of the population, and the inconvenience of disrupting people's lives and work would further damage the already unstable economy. It would increase unemployment, cause more people to rely on government help, the government would go further into debt, stock markets would plunge, financial meltdown, panic in the streets. Bad things ensue. And all because we wanted to combat cancer as best we can.