The idea is that you would use this in situations where you currently would offer a "reset password via email" option - since this means you already treats control of the email address as identity.
But anyways, my impression from reading the page was this is not just used as a password reset scenario but as a general login method.
Which if you agree with, leads us back to the scenario where authentication & authorization lies solely with the email account, which if compromised is the single point of failure.
I would appreciate it if someone were to help point out what flaws there in this line of thought rather than a straight downvote with no explanation.
In effect, any site that offers a password reset via email is already using your email as your identity.