Now that people are carrying mobile, internet-connected computers around with them basically all the time key signing can be automated.
The question of "does the person standing in front of me control a particular private key" can be answered by having each person's smartphone sign a challenge and exchange keys via QR codes (bluetooth, NFC, etc). This step should require very little human interaction.
That question, however, does not establish an identity as we humans understand it. Identity between social creatures is a set of shared experiences. The way that you "know" your friends is because of your memories of interacting with them.
Key signing should be done in person and mostly handled by an automated process. Identity formation is done by having the users verify facts about other people based on their shared experiences.
If properly implemented the end result would look a lot like a social network that just happens to produce a cryptographic web of trust as a side effect.