Insurance potentially protects people from fuckups with the sending of the money, like "we sent $900M to the wrong person and they won't give it back". If the bank collapses, the individuals holding accounts at the bank are covered (to a point) by the FDIC.
Funny you should mention that. If the money is sent, and there is a clear record of it having been sent ( especially via wire ), I am not sure how easy would it be to claim it under FDIC umbrella if the bank collapsed. FDIC is for the money in the account.. although I am sure that is a fascinating question for a lawyer.
edit: The reason wire fraud is so popular is basically, because once the money leaves the account, the recipient has to agree to return it. You can imagine fraudster likely will not.
FDIC insures the individual deposit accounts up to some maximum per account type. Say Citibank only had 900M and they fat fingered their own 900M as principal payment on some loan they are administering, then it could lead to a collapse of Citibank. In the most recent case the judge let it stand so Citibank has to absorb it and now becomes the de facto lender to Revlon now I guess. I imagine there must be some contract stipulations to Revlon / Citi or Revlon needs to negotiate. If there aren't, then Revlon got a sweet deal but I imagine all new loan related documents got updated to reverse this kind of thing in the future. If Revlon acts like they got 900M in free money well then the company will go out of business because no bank will work with them again. I imagine they will get a nice interest rate though since they have leverage now.
For the average person, I wonder if this means that if your mortgage servicer or your say student loan servicer does the same thing and inadvertantly pays off your loans that they then can't come back at you.
Citibank did not fat finger. They have have made an appropriate transfer to an appropriate destination under an incorrect internal book keeping line item. That's why the case was not about a wire being reversed - rather it was the case if the under their agreement with a customer that not on schedule payment could have been used by the customer to complete a transaction.
FDIC does not protect you from sending money to the wrong person. It only protects you from a bank going insolvent because it lent out more money than it has. That can't happen in Bitcoin, because your wallet doesn't lend your money out to other people.
Bitcoin wallets don't lend your money out to other people because they aren't corporations trying to make a profit. They are just wallets, doing a service for you.
We've come to rely on using banks when we want to send money to other people because USD alone doesn't know how to send itself to other people online. So banks have stepped in to fill that role. Now we can't even pay for things without a for-profit bank existing in the middle of the transaction. And that bank tries to make money by lending out your money to other people, and that gives it a risk of going insolvent, and so FDIC was created so that the government takes the risk of banks going insolvent.
If you send money to the wrong person, a bank may or may not be able to get your money back. It depends on the bank, and how well they know the other person, and what method they used to send the money, and how strong the threat of lawsuits is between the two parties. None of this has anything to do with FDIC, which becomes totally irrelevant when you use Bitcoin.