That’s exactly what ‘log in with your Google account’ on most newer websites is for.

It’s actually better than what you described in your article, because you don’t need to check your email before accessing a website and are authenticated via a cookie / your browser.

What’s worse, the way you describe your idea makes it sound like anyone who can interrupt your mails can now access your account. Unless the mail is sent encrypted (and sadly almost no one does this) it’s pretty easy to interrupt and steal the link inside.