> "what was the hardest day of your life" is a pretty standard

I would suggest that this is a misremembering. As someone who's hosted thousands of interviews at companies big and small, all of the questions were scoped to professional work. Why? because when you ask things like "what was the hardest day in your life" you have a non-trivial chance of getting your interviewee tell you about the time they saw someone die, cleaned up a suicide attempt, or developed a new fear. That or you see someone make something up on the spot.

Its just not a useful question. If they answer honestly, then they are going to just going to remember that sad feeling of re-living trauma. If they don't answer honestly, they are more than likely going to be pissed off at the weird prying question.

These questions are emotionally expansive, you could have been getting on really well, shared a joke, had a great conversation. All of that will be blotted out by remembered pain.

The reason why people ask "can you tell me a time you overcame a big obstacle to achieve a business outcome" is threefold:

1) can you describe a blocker with the right amount if context

2) can you talk about improving things without insulting the people blocking you

3) can you think of ways to non-destructively overcome problems

Asking about when your pet died doesn't give you useful information