My classes in finance said that rule #1 is to make your payroll (followed closely by pay your taxes). Failure to do this - even when the problem isn't cash flow, but IT failure - is inexcusable. It's the CIO's job to ensure that any risks to this are mitigated.
A lot of organizations, the company culture becomes so entrenched that almost no amount of C-level meddling will make a big difference. And this is especially common in government organizations (and in companies with very strong unions).
Fire them all. For cause.
Errors of this magnitude are either a symptom of some deep-running problem with an organization, or (much less likely) freak accidents.
In the former case, random firings aren't very likely to improve the organization; in the latter case, you'd be firing the people best qualified to do a post-mortem and making sure the same or a similar failure never happens again.
The rest of your post is more of the same “it can’t possibly have been me!” This isn’t a the website went down problem. People didn’t get paid here.
Dilution of responsibility is a real problem, but harsh punishment of everybody that, under some (your?) metric that made an error is definitely not the solution.
If you're truly interested in this (and not just angry and looking for somebody to take it out on, even though the root cause here is probably systemic – which is not the same thing as "inevitable!"):
The aviation industry and its culture of failure analysis and prevention is a great place to start, in my view. We have a lot to learn from that in our industry.
Important to note that this has been largely diluted in the US via regulatory capture, leading to things like the 737 Max disasters - so looking at the aviation industry a few decades ago is probably the way to go.
I believe that this USPS situation is a degeneration of internal fights that are lasting more than a decade now.. it is about money and authority, indeed