You would think. The issue no one seems to think about is that you need to make sure to pay for the domain for the duration of your life(at least). Otherwise, as soon as you lose your domain you lose ownership of your email. Any one that has control of the domain has control of your e-mail.
This dawned on me after a place I worked at reactivated the email I used for work when I worked there. It has my name but I have 0 control over it. Lucky for me I never used the email for things other than work so it's not a big deal. It is still bothersome that they can do that and I have no say so on its use.