It's tricky, because an insurer of your body (for medical care) has a vested interest in you taking good care of it (health care). By offering to pay for these services, they can potentially realize savings by not paying for the surgery that your undiagnosed diabetes or heart disease or whatever resulted in later on.

And since this is capitalism, if one guy offers that (an obvious benefit, or so it seems at least), their competition must do the same. Now the marketing department has us convinced that insuring only for major expenses (high deductible plans, basically) is stupid and that good coverage means only paying copays (which are also on the rise, duh). And it's easy to convince the public of that because paying a $35 copay for a 10 minute exam is still an easier pill for most of us to swallow than $100 or $200 self pay for same, since we're not thinking about the $15,000 premium which can be made nearly invisible to the consumer if their employer is paying for it, etc. Numbers made up of course, but I think the scale is reasonable.

I don't have all the answers, but I do think it's obvious that capitalism is not the correct approach if your goal is a healthy population.