Ah! The idea is not for people to just go live on Mars as a replacement to Earth. I agree that is unrealistic on anything even remotely reasonable as a timeframe. Rather it's the opposite! Like you mentioned, even in scenarios that kill effectively 100% of people on Earth, it would still be a far more hospitable place than Mars, with very few exceptions.

So the idea of a backup is not that we just go live on Mars, but rather that we have a significant number of people on Mars (and elsewhere ideally) that can return to Earth in such a scenario, help restore order, find/rescue survivors, and generally get society going again. It's simply the planetary equivalent of being able to send in aid to an area after a catastrophic force majeure.