The number of acceptable deaths in this scenario is the whole of humanity-2 (or even 0 if we have machines that can keep the colony functional while growing the next generation of tube grown humans), since the scenario otherwise is the extinction of humanity. I'm not talking just about the situations where Earth survives as a planet. There are things out there that could destroy the planet itself. In that situation no amount of caves will save anyone there.
As for the quality of life I repeat, volunteers. People are willing to do many crazy things if it means they get to do them first. And why do you suddenly forget about caves when it comes to other planets (or moons)? If they can live in caves on Earth then they can live in caves elsewhere. That helps with the whole radiation and no children bit, so the situation suddenly becomes not so pointless.
Again your plan only includes the fairly benign disasters that could happen, and even for those you're wildly optimistic. Exactly how many shelters do you think humanity is likely to build? I'd be surprised if we even reach enough for a million people to survive for a few months unless there is a clear indication that something is going to hit us (and by that time there is likely to be no time to build anything new). Just look at what such relatively common disasters as tidal waves or hurricanes can do and how well humanity is prepared for them. (BTW how would you decide who goes into these shelters, since you're so worried about discimination).
The point of the offworld colonies that they can function as shelters for humanity without that being their primary purpose. They can be built as research stations or even eventually for profit, but still save at least some small number of humans in case something very bad happens.