What you have is not considered health insurance so much as disaster insurance.

Similarly, what is considered health insurance is not really insurance but a convoluted way to pay for healthcare. I think there's a place for what you're calling disaster insurance but to me sounds truly like insurance for health-related issues (i.e. risk-pooling high cost low probability events). The conflation with what we've got now with that is one of the key reasons our health care system is so out of control, in my opinion.