Your question implies the following:
- The we know what a functioning and healthy society looks like and, thus, know what next step we're missing to get there.
- That there is anything like a consensus on what the "most" important problems are or what their approaches should be.
- That these are problems with direct solutions in "technology," without cutting-edge domain-specific knowledge.
I'm not sure that any of these is strictly true, and I'm nearly positive that we'll only know most of those answers in hindsight.
How about race relations? There's no app for that. War? You can't solder-up a PCB that convinces governments to stop murdering each other's citizens over differences of opinion.
Speaking of governments, what would a "techie" solution to government oppression look like? We have Tor, cryptocurrencies, steganographic filesystems, and mobile devices that would destroy the data on them before giving it up to an intrusive search, and look at how governments react.
That said, how about some of the areas where technology absolutely has worked on big problems?
Do you think climate change is a big problem? Do you think that the amount of power consumed by information technology globally is a terrifying figure in the face of anthropogenic climate change? This is a problem we know how to fix in "tech," and we're working on it.
Deaths due to traffic accidents? Computer vision and distributed coordination algorithms are at the core of self-driving automobiles.
How about 3D-printed prosthetics, or the medical industry in general? Data processing revolutionized drug research and genome work. Sure, there are more people doing silly apps than designing new systems for doing drug interaction simulation because one requires connections to established research labs, years of work, very expensive studies of efficacy, a decade of postsecondary education to have the domain-specific knowledge, and a hardware budget that runs into the millions; the other requires a crappy $300 laptop and some free software.
If there's a big problem out there that you want solved, either put up, pay up, or shut up.