It's not about emailing plain text passwords vs. a URL, it's about storing passwords in plain text vs. hashing them. Storing passwords in plain text is not considered secure because if the site (or server, or database...) is exploited, the hacker has access to the user's account on that site along with any other site on which they use the same username and password. A correctly hashed (and salted) password does not have this vulnerability.
A site that is storing passwords securely can't email you your password, because it doesn't know what your password is. That's why a non-guessable URL that allows you to reset your password is sent instead.
If the system you're securing is sensitive enough that you want to protect users from having their email hacked, consider using two factor authentication for an added layer of security.