Email address as website login ID

More and more websites are allowing you to use your email address as your website login ID or user name.  This is good.

What is not so good is that email addresses change over time.  Now, hopefully you can change the email address that the website uses to send email to you.

However, today I encountered a website that allows you to change your email address - but not the user name, which was the email address that you had when you first registered with the site.

So I am now in the situation of

a) Having to login with MyReallyOldObsoleteEmailAddress@defunct-mail-server.net

b) Getting email sent to newaddress@current-mail.net

:-(