The theory underneath self-punishment is that it prevents recurrence. It does not appear to. People who are harsh with themselves make roughly the same number of mistakes as everybody else and spend considerably longer in the aftermath.
Think about what you actually do when a colleague sends an email to the wrong person. You say it happens, you help them fix it, and by Thursday nobody remembers. That is not softness. It is what makes the fixing quick.
The same arrangement is available internally, and is usually the last place anyone thinks to apply it.