A company is bound to fire people in a well functioning economy or the alternative is every single employee will lose their job when the company goes bankrupt. Some people would rather bring every company down to the ground before firing a single person. In a well functioning economy what you then want is a short worker reallocation time.
Also if one of your options for "taking responsibility" is quitting, I guess your view of the world is that you would also fire any of your employees when they mess up, when whole industries have recognized the need for blameless cultures where making mistakes is part of the learning process.
You can fire people and/or let them go without claiming you "take full responsibility". That's ok, and exactly my point.
The phrase "I take responsibility" is never accompanied with any sign that the person does in fact take responsibility. It means more than just "Ooops, I did a bad"
Also if one of your options for "taking responsibility" is quitting, I guess your view of the world is that you would also fire any of your employees when they mess up, when whole industries have recognized the need for blameless cultures where making mistakes is part of the learning process.