How are usernames any different? You're saying identity is transient. This is true of every sort of identity except perhaps your soul. Regardless email addresses are more stable and unique than usernames. In fact they are just a username plus a domain that happens to have the ability to be routed messages in a standard way.
Of course you should be able to change the email on an account. Usernames can also be changed and are far from canonical. Your point about emails is not invalid, it's just not addressed by usernames, and usernames are actually inferior in that respect.
So, I did not use the word "username" in that comment you are replying to. I thereby will assume you mean "stable and opaque identifier assigned and chosen by the authentication provider", which is what I would argue for (as opposed to attempting to rely on an e-mail address as a stable identifier).
I did use the word "username" in a response to someone else, but that was a very different (and much more abrasive :() argument path.
> Regardless email addresses are more stable and unique than usernames.
E-mail addresses are not more stable that usernames, because e-mail addresses have an external purpose: they receive e-mail. Many people actively go and change their email addresses periodically in order to stop receiving e-mail from people they previously were receiving e-mails from.
A "username" (your word here), especially (and maybe specifically) the "good" kind that is never shown to another user and is just used for account canonicalization, which conceptually could be a random number assigned by the system, is something that the user has no reason to change unless they actually want to never log in to the account again.
E-mail addresses also are tied to the DNS system, which other forms of identification need not be: you can instead tie them to a private key kept by the authentication provider. That would make "me" be A@B where A is a number and B is a key pair. In this way, even if the way you continue to contact my authentication provider lapses (such as attempting to use a hostname) only if the new owner has the same key are they able to claim the identities there (unlike e-mail) and as the user specifier is opaque (not a string that I'm going to care about and want to make pretty, or something I'd ever want to change unless I actively want to lose access to my account) it will not run afoul of the problem with e-mail where people feel compelled to reuse them after some time of abandonment.
The problem then with Persona is that it is the websites consuming it who have the onerous job of dealing with every possible e-mail address change a user may request. With more classic attempts at federated login, users may end up with multiple authentication providers that can become somewhat confusing, but they demand to change authentication providers and especially lose access entirely to authentication providers sufficiently rarely that it is a non-issue to handle the support load of helping users remap their accounts (something that is difficult to automate, of course, in the case where the user already lost access to their old identity). With Persona, this is now something that the user has to do when they change e-mail addresses at every site they may ever have logged in to using their account, ever. :(
Of course you should be able to change the email on an account. Usernames can also be changed and are far from canonical. Your point about emails is not invalid, it's just not addressed by usernames, and usernames are actually inferior in that respect.