You would get a random code or several codes you print out and put into a safe place. If you ever forgot your password, you would dig it our and supply to the website to trigger a reset (which could include or not include email-based verification). The codes would only be usable for passwords resets.
That is, the Persona "forgot password" is a single point of failure which, if compromised, can provide access to a whole ecosystem of sites. And it will be tied to your email account.
Maybe it would help if we considered two hypothetical scenarios. A: Your email is compromised, and you're registered on 15 websites with that email, each of which has a "forgot password" option. B: Your email is compromised, and you've used Persona to sign into 15 websites. In what concrete, practical way is B a more damaging situation than A?
1) Fight to get your email account back
2) Visit each and every site and manually recover your account