One of the ways crackers gain access to a user's email is by guessing their password, a simple task when a huge number of users use the same password everywhere. With Persona, only your email provider (and the persona.org fallback) have your password (two passwords in the case of the fallback), hashed or not.
If you're already a password ninja and use a different and unpredictable password on every different site without forgetting them, Persona isn't an improvement in security. If you don't, as most users don't, Persona makes authentication more secure and more user-friendly at the same time.
With Persona, your weakest point would still be your email provider, which is why it would still be wise to recommend two-factor authentication for your email.
If you're already a password ninja and use a different and unpredictable password on every different site without forgetting them, AND you have enabled two-factor authentication with your email provider, Persona IS an improvement in security. This is because, with Persona, having two-factor authentication for your email would automatically mean two-factor authentication for all your websites as well.
I use Two-Factor Authentication across a lot of my accounts. I feel a lot more secure when I can telesign into my account. If you have that option available to you use it, it is worth the time and effort to have the confidence that your account won't get hacked and your personal information isn't up for grabs. If you opt into 2FA, you will have to "Confirm your phone". You would receive a text message with a specific code to be entered into the system. If you don't want to do this every single time, you can designate your smartphone, PC, or tablet as a trusted device and they will allow you to telesign in without the text code. Should an attempt to login from an unrecognized device happen, it would not be allowed.
Your last point is not completely accurate; with Persona and 2-factor auth on your email account, you would then have verified ownership of your email account via 2-factor authentication. This doesn't mean that every assertion generated by your Persona account will have been generated with 2-factor auth.
If you're already a password ninja and use a different and unpredictable password on every different site without forgetting them, Persona isn't an improvement in security. If you don't, as most users don't, Persona makes authentication more secure and more user-friendly at the same time.
With Persona, your weakest point would still be your email provider, which is why it would still be wise to recommend two-factor authentication for your email.
If you're already a password ninja and use a different and unpredictable password on every different site without forgetting them, AND you have enabled two-factor authentication with your email provider, Persona IS an improvement in security. This is because, with Persona, having two-factor authentication for your email would automatically mean two-factor authentication for all your websites as well.