Comment: People would choose different price points for insurance

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In reply to comment: thanks for your response! Two (see in situ)

People would choose different price points for insurance

for the same reason they choose different price points for any product.
Premiums might vary due to several reasons - losses covered, deductibles, ease of filing claims, promptness of claim adjudication and payment, etc.

There is already a re-insurance market which is in effect an insurer of insurance companies - http://en.wikipedia.org/wiki/Reinsurance.

I can't speak to it's efficacy, but it's there.

You might ask your friend if it's OK to rob a solvent insurance company (its shareholders and policyholders) or taxpayers to pay the claims of an insolvent insurer. If your friend supports legalized theft, you may be wasting your time trying to convince him there is an alternative.