A lot of email clients support multiple email accounts, or at least sending addresses. Not just desktop ones like Thunderbird, but web ones like Gmail too.
You can additionally set up email to be forwarded (or retrieved). So, for example, you can easily have your me@example.com account forwarded in to Gmail and Gmail set up to send from that address.
That works fine if the site sends a confirmation email, it'll get to Gmail where the user expects to read it. But the other way around will give the user errors about having the wrong email (even if tj user picks the right outgoing address, because you won't be able to verify it), and ultimately cause the user to give up or you're going to have to spend a lot of time supporting all kinds of weird email configs.
You can additionally set up email to be forwarded (or retrieved). So, for example, you can easily have your me@example.com account forwarded in to Gmail and Gmail set up to send from that address.
That works fine if the site sends a confirmation email, it'll get to Gmail where the user expects to read it. But the other way around will give the user errors about having the wrong email (even if tj user picks the right outgoing address, because you won't be able to verify it), and ultimately cause the user to give up or you're going to have to spend a lot of time supporting all kinds of weird email configs.