Their overhead is much larger than 3%, and that overhead is devoted to denying claims. The entire structure of the business incentivizes denial of claims. Medical care isn't suited to the insurance model anyway, among other reasons because the technology keeps changing and because moral hazard is inherent to all lifestyle choices.
Good insurance coverage increases unhealthy behavior in ways that can't be monitored.
There's also Krugman's point about the death spiral once premiums start knocking healthy people off the rolls.
