Would health insurance costs be lower if it was really for Emergency use and not checkups?

It seems like health insurance is a high cost item because people go in for every little sniffle, instead of when they are seriously injured or sick. Should Health Insurance companies pay for regular checkups and physicals, and pass the cost to customers, or should people just pay those out of pocket?
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Actually, healthcare cost a lot because companies HAVE to pay for people who do not have insurance, at the Emergency Room. (I have two EM docs in my family) Emergency docs get paid about twice what family practice docs do, and the overhead at an ER in the hospital is much more than a private practice. Our insurance could be much less if we'd just give everybody the freedom to have yearly checkups at their family practice doc instead of waiting until things get out of hand and expensive and they show up at the ER with a tumor or go there for a cold.
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