The recent wave of password and hash theft might become an incentive to move to this login method. I was skeptic about the possibility of BrowserID catching on, thinking the Google/Twitter/FB wouldn't give up tracking users with their ID methods. But if there is a way to make this widespread (though I can't imagine how) I'd really like it to happen.
Will Mozilla provide native support or an extension? Or they feel like it would hurt if someone could implement a bad login page that still works if the browser has native support?
Password/hash thefts have been happening for as long as there have been systems with passwords. What changed recently is that we now have centralized services with huge numbers of important accounts. There are more service with large number of accounts and more services that affect multiple aspects of your digital life. When someone steals hashes from those, the press and people are more likely to notice.
I think most people overemphasize the importance of the particular authentication scheme used and overlook the problems created by extreme centralization of stuff.
Will Mozilla provide native support or an extension? Or they feel like it would hurt if someone could implement a bad login page that still works if the browser has native support?