The closest I can think is the old scam where a business would mail you a package then demand payment for the item mailed to you. That was solved by just making anything shipped to you yours with no legal obligation to send it back

Unfortunately it doesn't work for instances of, say, a bank accidentally depositing extra money in your account, or their ATMs accidentally dispensing too much cash.

Why would it? The situations are entirely different; in the mail package situation, the outside company is attempting to get you to pay for something that you did not request. In the Bank/ATM, the company made a mistake.

For the bank situation to work, they would have to add an unrequested service to your account and then attempt to charge you for it. i.e. Bank adds overdraft protection to you checking account and then bills you for it.

Say you have an internet plan with a 5GB download limit and after 5GB the connection would no longer send data, one month it lets you download 7GB and then they send you a bill for going over. You probably would not have to pay the bill since they changed their behavior and provided extra without prior notification.

Re:Optics, I agree, but I think they would be counterweighted by the dimension of the issue fixed.

To put a hypothetical example, if I fix a life threatening electrical or structural issue in a children's hospital unsolicited, whatever hit to my reputation I take by charging for unsolicited work, is dwarved and possible restored and reversed by the gravity of the issue fixed and the consquences avoided.

Of course this is contingent on whether the value was actually provided and whether it is provable.