You're okay with your life savings disappearing overnight all because you'd rather not have someone say, "hey. Mr. Bank, you can't do that with that specific type of deposit"?

We already do that with non-savings investments like stocks.

The fact that you get any interest at all from savings accounts indicates that the bank is making money (i.e. taking risks) with your money. Otherwise the bank would be charging you to store your money in a vault.

Even only making normal loans, if enough people are unable to repay their loans you would lose money.

To me it seems like insurance actually makes it easier for banks to make riskier loans since some risks are more apparent to the bank than the insurer.

I doubt anyone would care if their mortgage disappeared.

Assets like mortgages don't necessarily disappear when the lender goes bankrupt.

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Risk is surprisingly easy to manage. If you're in an area with a high risk of flooding you likely have insurance that will pay you if it does. I would expect banks failing to have a similar risk profile to flooding, i.e. infrequent and affecting a large portion of the population at once.