What is also "common sense" is the position that once the sale of something is mandated, the providers of that something have significantly less incentive to control costs.
Wrong. Where I live it is mandatory that every family purchase at least one car in order to get around. No, that isn't the meaning of "mandatory." Owning a car is a practical necessity in such a town. However, those that can't afford cars must do without. For instance, they must either walk, or depend on friends, relatives, and/or taxis to go from place to place. Others will economize with a motorcycle, or compact car. If the local government mandated car ownership, then there would be a spike in the price of low-end economy cars.
Your logic is lacking. Your notion that people ought to buy "health insurance" is an example of the fallacy of equivocation. "Insurance" is buying protection against bill you can not pay by pooling risk. "Health insurance" that constitutes "insurance" against bills you cannot pay are high-deductible catastrophic policies. Buying a typical policy is economic idiocy for those whom can risk-rate themselves as being low expected medical cost. Those whom risk-rate themselves as a poor risk, those with chronic conditions, etc., will be more than eager to pool their costs across the larger pool. Forcing everyone into such a pool is simply the mandating of the subsidy of the sick by the healthy, the old by the young, etc.