Banks are basically all software too now. They can have the exact same issues. They're not just taking your bills and storing them in a physical vault for you to take out later.
I don't know if this is right. Traditional money transfer is not some absolute, irreversible thing. It is the product of software yes; but more importantly, it is the product of trust between institutions and individuals, backed by government and the legal system.
In traditional finance, there is _far more_ than just the correctness software ensuring the safekeeping and transfer of your assets.