Regarding the interstellar space colonization question -- ultimately it's a question of whether we want our species to survive. In a billion years, the Earth will be swallowed up by the Sun's expanding size, and certainly will be obliterated when the Sun goes Super Nova. It's nice to think this won't obliterate the human species!
However, you ask a good question -- and one related to the 5 Whys: why do we want the human species to survive permanently? And are we just extending the timeline of an inevitable demise? This leads me to think about the heat death of the universe and then I get depressed. :)
In terms of social inequality and immobility, here we go:
Why #1: extreme social immobility and inequality often destabilizes a society. This is why I'd consider it a problem/threat. At the very least, many economists argue that social inequality slow down the rate of innovation and economic growth.
Why #2: when you look at Western capitalist societies there appears to be a strong correlation between social mobility and access to opportunities (e.g., education, health care, etc.) and a society's ability to innovate. Note that "innovation" here refers to the society being able to solve other problems affecting said society. In a sense, social inequality and immobility stifle innovation and thus, it is "meta-problem" -- it makes it difficult to solve other problems the society is facing.
Why #3: a lot of literature (in management theory, education theory, etc.) argues that giving people the ability to grow, develop, learn, etc. makes them more productive, creative, and better able to solve problems. Social immobility and inequality is a form of oppression, in this regard.
Why #4: this sort of mobility ultimately aligns incentives -- you are encouraged to be creative, solve important problems, etc. that are valuable for society because doing so will enable you to enrich yourself.
Why #5: because humans need incentives to succeed, and human ingenuity is something that need to be cultivated.
TL,DR: social inequality and immobility is a meta-problem because (a) it makes society unstable and leads to the other issues we are worried about, and (b) reduces humanity's ability to innovate and thus solve other problems.