If doctors, hospitals or pharmaceutical companies charge more than some people feel like paying, then the answer is price control. The actual track record of politicians, government bureaucracies, or price control is of no interest to those who think this way.
Politicians are already one of the main reasons why medical insurance is so expensive. Insurance is designed to cover risks but politicians are in the business of distributing largesse. Nothing is easier for politicians than to mandate things that insurance companies must cover, without the slightest regard for how such additional coverage will raise the cost of insurance.
If insurance covered only those things that most people are most concerned about-- the high cost of a major medical expense-- the price would be much lower than it is today, with politicians piling on mandate after mandate.
Since insurance covers risks, there is no reason for it to cover annual checkups, because it is known in advance that annual checkups occur once a year. Automobile insurance does not cover oil changes, much less the purchase of gasoline, since these are regular recurrences, not risks.
But politicians in the business of distributing largesse-- especially with somebody else's money-- cannot resist the temptation to pass laws adding things to insurance coverage. Many of those who are pushing for more government involvement in medical care are already talking about extending insurance coverage to "mental health"-- which is to say, giving shrinks and hypochondriacs a blank check drawn on the federal treasury.
There are still some voices of sanity today, echoing what Edmund Burke said long ago. "The study of human institutions is always a search for the most tolerable imperfections," according to Prof. Richard Epstein of the University of Chicago. If you cannot tolerate imperfections, be prepared to kiss your freedom goodbye.