I mean...if this were any other business, someone clicking the wrong button and then someone else not catching this error would maybe mean someone's account was accidentally closed, or someone receiving a free pizza, or whatever.

The IT systems within banks are more or less the same as IT systems anywhere. Just as advanced, just as crappy. The difference is that if there is a human error with banking software, you're not sending free pizza, you accidentally pay ouy $900,000,000.

Nothing about bank risk management is easy. You haven’t accounted for a whole host of risks with this simple analysis, including the most important one: customer retention. The high-value customers sending high-value interbank transfers won’t be impressed that our systems let their wire go out the door incorrectly. Even if I can totally reverse the transaction (and it’s not nearly as easy or guaranteed as you’re assuming) I still have to tell the client about it in most cases. The client will, correctly, think “what if they can’t get it back next time this happens? I’ll find a bank that doesn’t have these kinds of issues.” And aside from crimes, losing a high-value client is perhaps the worst offense you can commit in banking.

Regardless of the dollar amount or outcome I also have to tell the audit committee, the board, the auditors, and all of my regulators. And exactly none of those groups would let me put your write-up along with the conclusion “risk accepted” in front of them.

Most bank transfers are actually not reversible, except for some limited retail client (including small companies) operations where specific terms & conditions allow the bank to reverse payments to the extent possible, which they really prefer avoid using as it looks really bad for a bank whose most important asset is the confidence of its clients and counterparties. Reversal may also no longer be possible if the money has already gone out in a system that does not allow reversal, or if the client is bankrupt in the meantime (depending on local banking and bankruptcy laws and circumstances).

For any other payment system for larger sums / corporate and institutional parties, settlement finality is a huge thing that is the subject of all sorts of specific legislation, as it would be a real issue for the health of the financial system if a settled payment can simply be reversed, as it would have a lot of unintended consequences further down the line. So banks actually do have strict risk management policies to avoid wrong payments, but there are so many complex transactions for which ultimately a human (actually at least 2 due to 4-eyes principles) must confirm whether conditions for payment are satisfied and whether payment details are correct, and humans are always prone to making mistakes once in a while.

    Risk: An employee can transfer all of a customers funds to an oversees bank account
    Mitigation: Multiple employee must approve transfer of funds
    Mitigation: No individual employee can deploy modifications to the computer system actually doing the transferring.
    Mitigation: No team can both write code and access (the important) production systems
    Mitigation: Must stand on head while deploying code, because people standing on their head are more honest
    Status: Risk accepted, we'll have 10 more meetings to review this next month.

The idea that bank transfers are reversible is false. Some are, some aren't, the adversaries are interested in the ones that aren't. The idea that manual review is a trivial fix is very false. Even if there was a trivial fix, the idea that you could get this past the numerous gatekeepers with a simple and easy process is probably false in most banks.

Bank transfers between banks are not reversible.