There was (Still is!) something very similar in an organization called CAcert[1], which was a predecessor to the current Let's Encrypt project (free SSL certificates) that hasn't succeeded dramatically because it hasn't been able to get its root certificate into browsers.
Basically they host parties, usually alongside a Linux or BSD conference, where trusted members will look at your legal documents and then affirm on their website that you are who you say you are. Some amount of "you are who you say you are" was then needed to get a free SSL certificate.
But imagine that in this context: everyone keeps one secure CAcert account, and then when you need to reset your password, some sort of OAuth handshake with CAcert proves it. You have one secure account with CAcert, and all of your utilities and cell phone stuff and PayPal will only reset your password with a handshake with the CAcert servers.