If my friend can sign a message using the same key on both services - and I already trust that key is them - I can be almost certain it is them. Regardless of the service.

This is one of the first use cases for keybase.io - verifying identities across a few main social sites. (E: For clarification, Keybase makes it easier to find these proofs. It isn't necessary as part of the proofs.)

For example, you can find me on Reddit or Twitter and know it is me. You can also see my website URL and know that I own it - and a bitcoin address where you know I will receive the money. This is because I've verified that I own these accounts using PGP - and I've done the same for HN in my user profile. See: https://keybase.io/nadya

It's only 'solved' if you don't care about usability. PGP quickly becomes a nightmare when you consider the day-to-day things 'normal' computer users will go through (private key stolen, password to private key forgotten, phishing attacks to sign replacement keys for friends, etc).