Hmmm. And would the insurance company come under the 'too big to fail, too big to save' soubriquet? Where is it based and who is it? Swiss Re, maybe? A company that has seen its share price fall by 60% on losses due to bad assets... AIG perhaps?
My point is that the same risk is extant whatever mechanism you use. Either money is guaranteed in the end by the state or it is not.
It certainly is! I've tried to give up worrying about it, but it doesn't work. So now I alternate between "don't care" and "press this button in an emergency". It at least gives me long periods when I don't worry about it!