We used to do that with a classifieds website. Not a code, but a link to click for authentication. To be honest many users didn't understand the concept. Emails

We used to do that with a classifieds website. Not a code, but a link to click for authentication. To be honest many users didn't understand the concept. Emails can be 1-2 minutes or sometimes more delayed. Users asked where they can reset their password. By being different we added confusion. I worked, 1000s of users signed up (free service), but we spend more time than we think justified on support emails.