If we ever reach a point where we are capable of establishing a permanent, self-sufficient colony on another planet, it's difficult to imagine that such a civilization would be unable to deal with any potential calamities on Earth itself.
What event could possibly make Earth less hospitable than Mars? Even assuming nuclear Armageddon or an extinction-level asteroid impact, you're still left with an environment much closer to habitability than what you would find on Mars.
It's really not just about "one backup colony" but rather the beginning of unlocking the abundance of the Solar System to improve (and move!) life, foremost because you think that when it comes to civilization you believe that the best days are still ahead of us.
Take the 7B people on Earth, and assume they're all families of 4. Put them each on 1/4 acre of land. Say that additional infrastructure like roads, schools, and retail will take an extra 50%.
That gives us roughly 1 million sq miles to hold the entire population of the planet on a comfortably-sized lot. That's 1/10 the size of the USA, about the size of the land area of Alaska plus Texas.
The people aren't going to be the problem with land usage.
What event could possibly make Earth less hospitable than Mars? Even assuming nuclear Armageddon or an extinction-level asteroid impact, you're still left with an environment much closer to habitability than what you would find on Mars.