Okay...I'm with you.
Now why does it need to be taken beyond what Mozilla offers? Let me go back and re-read your first post.
Ahhh...you want to keep track to be sure an email address isn't reused.
But that is an ENORMOUS CONFLICT with this statement in your second post:
using two browsers, one registers twice.
How does that work, if an email address can't be used more than once? How many users keep around as many email addresses as computers where they might login?
I know that I login to CodingForums.com from several different computers during the course of a month. So I would need a different email address for each computer??? I happen to have the capability to do that, but I would sure hate it!
I'm trying hard to see the advantages of this system, but I'm not there yet.
And I see nothing that says it is bad to remember *HASHED* passwords on a server. (Presumably we are talking about a "one-way" hash, meaning that a password can never be recovered, only tested.)
Hopefully others here will chime in.