Persona harps on 'your email address is your id' part, but it's just a way to get an identifier @ a domain (so your login id doesn't actually have to be a real email address). At this point, persona (or the service implementing persona, more precisely) will ask the domain to authenticate the identifier.

Using the mx record would be bad, because, if you are doing it yourself, then your email server would have to also have a persona authenticating server, it would be hard to use your own persona authenticating server and have a third party take care of email, etc.