Ignoring every other benefit and concern, verification in the way proposed is a bad idea because part of the verification process in most cases is verifying that the service can send messages to you that actually get delivered. If you do this and then send the first "log in link" email which gets held up as spam or putatively malicious since some server has the temerity to not be located inside the US, doesn't have a DKIM signature, etc, you haven't really verified everything that you need to know. Of course, those things can change at the drop of a hat anyway, but I'd rather have verified that 1 time than 0 times.

If all you do is use it for login and will never need to send a message, then fair enough, the email is just essentially a random string you can prove ownership of, and your ability to send messages that will be delivered to the corresponding mailbox is incidental. But that's not a general enough conclusion to hold for why "we" (all cases) should do it that way.