And if one starts applying your principle at a workplace, you end up with the whole company being afraid of doing anything at all, to avoid being fired.

No, there is a level of competency where once you make mistakes below that, firing is the right move.

If a surgeon keeps killing patients because he keeps forgetting to wash his hands, then he needs to be fired.

If a developer skips all company policies and deploys directly to production without a good reason, then he needs to be fired.

There are reasonable mistakes, then there are errors resulting from wreckless actions indicative of a larger problem with the person's view towards their work.

It is not hard to distinguish between someone who makes a rare, but totally understandable simple mistake, and someone who regularly screws up significantly more often than everyone else. Being tolerant of mistakes makes you a good employer. Being tolerant of regular incompetence makes you a bad one.

Make one mistake, it's an expensive training lesson.

Make the same mistake again, you get fired.

That is the wrong question. The real question is what did they do to ensure that this mistake cannot be made again by anybody. In the form this variation is in, the real question is what changes were made to the design so that the system cannot be over pressurized in that way by mistake.

Sometimes you can put in all the checks and balances you wish, but humans will just make a, well, human mistake.

All commercial aircraft have checklists in place, and a two person cross checking system in the cockpit, as well as mechanical means to detect potential problems - but aircraft still every now and then land with their gear still up etc.

Does it make economic sense for an organisation that has invested possibly millions of dollars in training a pilot to immediately sack him/her for a costly mistake like this? Sure, disciplinary action and possible demotion within the ranks is a given, but will you get rid of the one person who will be almost fanatical about never landing with the gear up again?

If they consistently make technical mistake and are sloppy in their airmanship, then sure, fire away. But it is going to be pretty much impossible to design a 'system' that can prevent human errors from creeping in.