The UK actually made it work in conjunction with identity federation through the Government Gateway, but then the Government Digital Service got hold of it and destroyed any chances of moving it forward.
Having seen it work I believe PKI can be practical at scale. And this is why I'd hoped a chat app might break some ground here.
And above you're saying it's about meta data problems in messaging systems. What is PGP's bad meta data story you were referring to?
Essentially, for most PGP workflows, PGP encrypts the body of the message but the entirety of the metadata (things like sender, recipient, subject line, basically anything you’d think of as “metadata”) are fully unencrypted.
If you believe that this webpage was delivered securely to your computer, then PKI might be practical. Of course, there are a few implementation details with that PKI.