Unless you happen to move in extremely well-informed circles, most of the information about what's going on in the world is coming to you through those little screens (or from people who got it from said screens)

True for larger issues, which makes moving in such circles so valuable and the perspective of people only looking at small screens potentially so distorted there.

However, for smaller issues and local community issues "special access" isn't really much of a thing.

Yeah, but then those smaller issues aren't usually contested. Humans are good at getting the directly and immediately relevant things right, where being wrong is experienced clearly and painfully. We have time-honed heuristics letting us scale this to small societies. Above that, things break down.

Not really: go to any meeting on building a new local road and see very different views on the local reality. The ability to understand and navigate those isn't too different to what is needed on bigger issues.