I doubt there's any case where mars is a better choice other than the destruction or the beginning of the physical destruction of Earth. The one possible plus is that if can survive the extremes on mars we will be able to survive them on earth too. The real win in having these large goals is not the achievement itself but what we learn along the way. Things like new tech,new uses of old tech and even how to better get along with each other not necessarily the achievement of the goal.

It's a place to vist but you wouldn't want to live there.

Mars doesn't make a ton of sense as a backup earth because gravity there is too weak to carry a fetus to term. If we had the tech and the urgency to terraform mars, it would probably make more sense to put those resources into space stations where we could control the environment better (and less risk from losing any one station). Mars in this scenario is sort of like an offshore oil rig that people work on for some months at a time and then go back to their life in space (again provided we can't live on earth for some reason).

I literally can't imagine a realistic scenario where we are better off on Mars.

Earth would have to lose its orbit and be falling into the sun or spinning off into deep space for that to make sense. It would probably be easier to deflect a meteor the size of earth that is headed for earth than to terraform Mars.

If terraforming becomes unbelievably easy then that would change the calculus - but then Venus might seem like a better candidate at that point.

False premise. Terrafirming Mars is a necessary prerequisite to any kind of tinkering on Earth. If you haven't practiced on Mars, how will you gain the necessary experience to be trusted to do anything on Earth where the consequences of failure would be extreme?

I always consider living on Mars or a space station to be much like living on a submarine, but without any time off. It seems likely that most people would go crazy, so even if you are not, others are. Your abiding question would be: what is the point?

Nothing. Absolutely nothing.

"The tech" is so far beyond what we can do that we would have self-contained cities in the Gobi desert, on Antarctica, and likely underwater and underground too, long before we can think of terraforming Mars. Even a dinosaur killer wouldn't be enough, while a supernova explosion like the one proposed as the trigger for the Devonian and Ordovician extinction events would also affect Mars.

As others have long pointed out, the population on Mars would need to be in the hundreds of millions just to have enough people with enough specializations to build and maintain the the equipment, and train those people, and the medical staff who take care of them, and the caregivers who raise the babies, along with the farmers, and plumbers, and everyone else. See https://www.antipope.org/charlie/blog-static/2010/07/insuffi... .

Or we hand-wave and say the tech is so advanced that computers do everything, in which case, why Mars when the magic tech can let humans live anywhere?