This is a great idea, and hopefully browsers will adopt it directly one day. In the mean time, this plugin is a nice way to test the concept.

I have a massive collection of passwords in my LastPass plugin, and managing them is a real mess. Sites are always changing their login URLs or doing other things to break the experience. Most of my family just uses the same password for all their logins, rather than deal with LastPass. With this new mechanism, you only need to store the private key, which is far simpler.

If a hacker steals your password from the server, they can log in as you. If a hacker steals your public key from the server, though, they still can't do anything. They need the private key to actually log in. So, besides being simpler, this new approach is actually more secure.