On the other hand, insurers probably have better actuarial data because of annual checkups and can better align their profit margins with fees. Thus reducing their own reinsurance fees.
Imagine you are an insurer and advise free annual checkups. Some of your patients don't bother. Those patients have a higher mortality. You conclude the annual checkup is good.
But you might be deceiving yourself - the kind of people to ignore health advice about getting an annual checkup might also be the kind of people to ignore the health advice on the back of a cigarette packet...
I'm not aware of insurance companies being too keen on getting into medical experiments like 'people with a birthday on a Thursday don't get the free annual checkup'.