Most people, for most things, don't need to verify trust outside of normal government channels.
i.e. any business I correspond with, trust is via the government that they are a business bound by the relevant legal system I live in.
Same story with communicating with basically anyone: if their GPG key was signed by the common government key, then hey, good enough for anyone.
The problem is...we don't have the infrastructure for any of this. And GPG key servers are inadequate for maintaining suitable privacy for people if they were used at this scale.
But we certainly could provide the means by existing technologies: e.g. nothing stops us making drivers licenses and other forms of ID smart cards.