People working in systems safety work on (at least) two levels:
1. Physical
2. Social
On the physical side they try to establish controls that prevent or mitigate issues or minimize the consequences of them. For instance, a modern reactor (probably, not my domain) is going to be designed in a way that certain meltdown situations can't occur (physically designed to separate reactor materials at certain thresholds, resulting in an automatic shutdown versus manual) or are properly contained (smaller reactors where a runaway reaction is more easily contained with modern materials at a reasonable cost).
On the social side there is training, regulatory controls, and an emphasis on safety culture/discipline. Discipline doesn't scale, but you can't totally avoid having it. This would be things like not turning off an alarm because it disrupts your nap (looking at you, Homer J. Simpson), but actually responding to it to determine its legitimacy (related concept: normalization of deviance). They'd also want to look at it from an HCI perspective and minimize false alarms and overwhelming operators with alarms or information that seem to be at the same level of importance, but aren't. So true critical issues are brought to the front as high priority, but less critical issues (ones that should be addressed but are lower priority) won't overwhelm the operator. (I've worked with others on this wrt avionics systems, alarm fatigue is real so you have to be choosy in which things get audible alarms and which get visual alarms.)
> If there's been an accident, the analysis is generally "we have to add sections in the manual for this specific scenario and we'll be safe",
In my experience, that's a belief held by the prideful and the novices.
> rather than accepting that it's impossible to prevent all errors and that it's merely a question of time before the next anomaly arises.
Anyone with a modicum of humility or experience will accept this and act accordingly.