Well, first of all, many health insurance plans don't cover routine care (annual physicals, etc.).
Second of all, those plans that do cover routine care generally do so under the theory that, by paying a small amount of money for routine care, they're avoiding paying much more down the road when the cheap problems that would have been caught at a routine physical turn into big, expensive problems.
Increasingly, health insurance plans cover routine care under the banner of "wellness" (there's a reason why there are specialized procedure codes to identify them). Unfortunately, they often take the form of "sure, we'll cover that prostate screening, but if it turns out you actually have cancer, um, tough luck."
Second of all, those plans that do cover routine care generally do so under the theory that, by paying a small amount of money for routine care, they're avoiding paying much more down the road when the cheap problems that would have been caught at a routine physical turn into big, expensive problems.