The risks are not 'car crash from doctors visit' they are 'got cancer from imaging', 'unnecessary surgery and complications', etc - the risks are directly related to the screening.
This is an active topic in medical ethics as well which you seem ignored of (no offense intended), given that you are framing this in terms of insurance or public health from the perspective of a beaurocrat - the bottom line is that if your screening is more likely to kill or maim you than the thing being screened for then that screening shouldn't be standard practice, and when it is less clear cut than that you still have to make a determination about which screenings make sense to perform on a population level.
That is something that a caring doctor has to think about as part of their duty, there is the very real potential to do much more harm than good by being thoughtless about the interventions you perform.