This is a variety of SPKI[1], right? I was thinking of a conventional PKI approach, with an adapted web of trust to verify identities [2].

You are right - theoretically this could work. But it would pretty much take a "boil the ocean" approach to make it work.

Browsers would need to implement a secure (private) keystore, and presumably some way to sync that to other browsers.

A whole new standardized authentication flow would need to be created, which wouldn't be the same as the existing certificate-based authentication (which no one uses anyway)

[1] http://en.wikipedia.org/wiki/Simple_public_key_infrastructur...

[2] http://en.wikipedia.org/wiki/Public_key_infrastructure#Web_o...