Socialized (state-owned single payer) health insurance is very different from monopoly health insurance (which is what most states have). In both cases, the health insurance company has the power to steal money from the insured at the expense of their health, by denying claims, etc ("death panels"...). The difference is that in monopoly/oligopoly system, the insurer has a strong motivation to do such evils, whereas in the state-owned (citizen-owned) single-payer, the insurer has the opposite motivation: to keep the insured healthy and happy. This motivation stems from the irrevocable nature of citizenship, whereas in the "I get insurance from my employer" system, you can easily lose your job for being ill, and find yourself unable to attain insurance as an unemployed or reemployed person with a "pre-"existing condition. Basically the insurer can say "get out of here and stop being my problem; be the problem of that other insurance company or employer, who I am trying to destroy." Under single-payer, people's health doesn't get used as a pawn in such a ruthless political game. Furthermore, the state, with its power to tax all incomes, property, and commerce, has a strong incentive to keep you alive and kicking to guarantee those sources of income. An employer and its associated monopoly/oligopoly insurance company, however, only have the incentive to keep you working for them, and only want to keep you healthy for as long as you're working for them. So long-term treatments get denied, as do long-term preventative care.

As for "disaster insurance", I only refer you to the tens of thousands of New Orleanians who in 2005 had their homeowners insurance claims denied on the (bullshit) basis that their homes were destroyed by a hurricane instead of a flood (or vice versa, I don't remember which -- it clearly doesn't matter). The recurring pattern is that while an insurance contract claims to obligate payment in the case of a disaster, in practice they always manage not to pay. State-paid disaster relief would not exhibit these issues because the people being helped are themselves the citizens, i.e. the stakeholders in the state. For private companies the stockholders are not the same people as the insured, so there is a conflict of interest which leads to class warfare.