I don't trust any "organization" to store and manage my passwords. A single subpoena to mozilla for a divorce proceeding or whatever could unleash cascading consequences upon you.
Plus, your keys are stored in the browser, according to callahad, so Mozilla doesn't have to know where you signed up: http://news.ycombinator.com/item?id=4232774
Also, in the future you probably won't even need to contact Mozilla anywhere in the process: your browser will store your certificates for you, natively.
Your identity provider just has to implement the BrowserID protocol https://developer.mozilla.org/en-US/docs/Persona/Identity_Pr...
Persona doesn't attempt to solve this existing problem.