https://medium.com uses it. And I'm working on a little project myself which will use this way of login.
About the frequency: there aren't many situations where a user has access to your application, but not to email. I've been thinking about that, but when you have access to a browser, (most of the times) you have access to your mail.
Instead of verification, you could use the emailaddress as a login-method. Don't use passwords, but let the users login by email, sending a mail with a time-limited authentication-token and make them login that way.
That way you don't have to deal with passwords, and you will know the user has a mailbox which they control.
I don't think it's a bad thing. It's a dangerous thing, but not bad per say.
The last years everything is changing to a "ME"-culture, of which this is also evidence. Respect for teachers is disappearing, and when a child gets bad grades, the teacher is the bad guy or woman...
I am a firm believer of a safe environment for children. But I also believe that complete freedom is not the solution.