The biggest issue is the whole idea of colonizing Mars or anywhere else as a backup runs into a couple major issues. 1) These backups are going to be extremely dependent on Earth for supplies because the alternative is replicating a tiny version of the whole planet's industrial base which will only make economic sense if transporting goods between these locations is extremely expensive, which is something that makes setting them up in the first place also prohibitively expensive. 2) Any technology that makes Mars/Space/etc survivable also makes it possible for an Earth based civilization able to survive basically any calamity up to the death of the Sun.
To your first point: yes, that's the whole idea and it's been the same playbook for any colony from the Americas to Australia. Mars is a much bigger challenge but our technology has advanced enough to make this possible. Let those who would dare risk their lives to achieve something great do so. If you don't want to participate then you don't have to, this isn't a national or international project so you can safely sit it out.
To your second: there are calamities for which a second self-sufficient planet would be necessary. A large asteroid impact would utterly wreck the global industrial base which is highly dependent on international trade and specialization of resource extraction and manufacturing in different regions of the world, having an independent backup on a different planet is one of the few ways to hedge against this. You could argue that every country on earth be fully self-sufficient and then maybe they could survive but that seems like a much bigger task since you'd be building multiple completely independent civilizations instead of just one. Guarding against another global pandemic is another and being out of range of nuclear weapons and their fallout is a third.
I bet an underlying thought is that we crabs will have to finance the entire Mars colony adventure through taxes and incentives and subsidies and whatnot.