[DennisP]

Even without underwriting it's still insurance, which is "a practice or arrangement by which a company or government agency provides a guarantee of compensation for specified loss, damage, illness, or death in return for payment of a premium" according to Google's dictionary.

[bradleyjg]

If there was a soup kitchen that charged something, maybe on a sliding scale, but not nearly enough to cover costs, it would meat the dictionary definition of a "restaurant". Calling it that would nonetheless be misleading.

[DennisP]

Yes but in this case, virtually everyone agrees with the precise dictionary definition of insurance and uses it in daily conversation all the time. Very few would agree with you that health insurance without underwriting should not be called insurance. Political discourse, everyday conversation, and the law itself still call it insurance.

(And while I don't think you meant the comparison this literally, I'll point out that health insurance companies do cover their costs. In fact, they're generally quite profitable.)