Something important about that situation is the power dynamic. You were not in a position of power, your boss was, and you were looking to defuse the situation and take ownership of a mistake. Your point is correct - there was a systematic failure at multiple levels of the operation that led to this being possible and even likely (too many hours, bad practices).

In such a situation, multiple mistakes were made. If that work culture could somehow support honest, open, and humble approaches to understanding the problem, there would be multiple people either apologizing or, better, taking ownership of their contributions and working towards preventing them in the future (the thing you identify that did not happen). Such a culture is, unfortunately, very unlikely due to the incentive structures of company hierarchy.

The role and power of the individual for whom we're setting these expectations is very important and it's very unhelpful that this isn't considered either in that wiki page or in so many comments (not yours, yours is good). Is the person that made a mistake very powerful and do they have a PR team? Their approach will probably be purely cynical. Is it a company? We should stop anthropomorphizing companies. Is it a junior colleague? Was it truly a personal error on their part or higher up or systemic? Was it a manager harming an employee? On a moral and societal level, we have to consider those harms and whether owning a mistake and apologizing is desirable or even sufficient - perhaps they should just be fired or we should consider their actions to be a crime. Or maybe "we" in this scenario is again PR thinking intended to protect the company, in which case the apology is carefully wordsmithed to avoid liability and has no real value.

If your primary goal is to minimize the damage of your mistake to maximize your political gains, then yes, you're right.

When dealing with actual, non-hypothetical humans, you should be able to set your ego aside to meet them on a human level and address them as such.

Too many in this thread fear of being perceived as weak, but I find that being an unapologetic asshole is just as bad.

The problem is that some people will perceive you as weak when you admit having made a mistake, and will exploit that weakness, if only to throw cheap shots when given the chance. It creates a real incentive not to disclose mistakes in the first place.

Is there any point in addressing the "mistake" if no one has the need to take responsibility for it?

Life is full of situations where no one acted unreasonably but something undesirable still happened. It's especially common for no one to see a potential problem, and thus for no one to be assigned the responsibility of dealing with that problem. If you have any stake in the overall success of the team, it doesn't matter whose fault something is, you just want the problem fixed.

Yes, 100%. In the parent's example the system should be fixed so that no one can push directly to prod. Failing that, some sort of standardized checklist/process should be put in place. That's true regardless of who personally pushed something they shouldn't, and would be true even if no one ever made that "mistake."