By passing laws to force insurance companies to cover things that have nothing to do with risk, politicians force up the cost of insurance.
Annual checkups, for example, are known in advance to take place once a year. Foreseeable events are not a risk. Annual checkups are no cheaper when they are covered by an insurance policy. On the contrary, they are one of many things that are more expensive when they are covered by an insurance policy.
All the paperwork, record-keeping and other things that go with having any medical procedure covered by insurance have to be paid for, in addition to the cost of the medical procedure itself.
If automobile insurance covered the cost of oil changes or the purchase of gasoline, then both oil changes and gasoline would have to cost more, to cover the additional bureaucratic work involved.
In the case of health insurance, however, politicians love to mandate things that insurance must cover, including in some states treatment for baldness, contraceptives and whatever else politicians can think of. Playing Santa Claus costs a politician nothing, but it can cost the policy-holder a bundle -- all of which the politician will blame on the "greed" of the insurance company.
Insurance companies are regulated by both states and the federal government. This means that, instead of there being one vast nationwide market, where innumerable insurance companies compete with each other from coast to coast, there are 50 fragmented markets with different rules. That adds to the costs and reduces the competition in a given state.
When there are innumerable insurance companies, it is by no means clear that political regulation of them will produce better results than the regulation provided by competition in the market. In a competitive market, insurance companies would cover only those things that their policy-holders are willing to pay to have covered. Policy-holders would have no reason to pay to have insurance cover things that would be cheaper if paid for directly -- or not paid for at all, in the case of things that are not a real concern to many people, such as baldness cures.