Is it worth living if you're locked inside a tunnel in a place where you can't even go outside, where you're only with a handful of people who will hit a genetic bottleneck in short order, where you're unable to then move from your extraordinarily fragile location to another one? It's not like we're going to have the variety of heavy industries required for creating spacecraft available on the near-atmosphereless planet where you basically need to stay inside all the time.

If something wipes out Earth, we're screwed. It was nice being here, but it's over. Whatever made Earth so uninhabitable that it makes a colony on a barren planet the only remaining splinter of humanity, isn't going to leave Earth in a recolonisable state.

It's not to say we shouldn't reach for the stars, just that I think the justification "save the species!" is massively overblown. If you really do want to "save the species!", then you're going to be far more effective in spending that space travel money in other areas: identifying events that cause global catastrophes and working on technologies to subvert them. Sending a person to another planet is amazingly expensive; setting up a self-sufficient colony even moreso; and setting up a colony that is capable of self-sufficiently colonising other planets more expensive again.

Not to mention that the social elites that will get sent to these colonies (shipping people is expensive, so you want to front-load skilled people) are also going to have to want to rear the number of children required to repopulate - and if you're not significantly expanding the population with each generation in such a case, you're making another extinction even all the more easy.