We mostly know the solutions to fixing the most oppressed or otherwise defective parts of the world; we just don't find it worthwhile to implement those solutions. I could solve 90% Equatorial Guinea's problems for <$10mm and a promise of immunity from prosecution or extradition by major world powers (i.e. places I'd actually be, afterward). Scaling that up for other countries is possible, too. For problems not requiring a ballistic solution, Bill Gates is doing a seriously effective job of solving the polio problem, and major headway into malaria.
The solutions to the most defective countries are all pretty straightforward and widely known; it's figuring out how to turn decent but not ideal countries like Pakistan into really stable first-world countries which would be hard, or figuring out how to stem the long-term decline in the US. (Yes, there are implementation difficulties in a place like Somalia, but it's because the benefit isn't worth the expense in blood/treasure. The cheap solution is to let the 1% of people who could make their lives a lot better by leaving do so.)
The skills required to solve the harder sociological problems don't really have much overlap with the skills to send people to Mars.
Bringing those places up to standard doesn't really give you anything new, although it does help those people. Putting humans on Mars is something we've never done before, and could lead to amazing technologies and opportunities for humanity. Just like I'd rather be a medical researcher than a family practice doctor, I'd rather push the limits of what's possible vs. contribute to more widespread adequacy, although both bring up the mean. I'm glad there exist both kinds of people, though.