Um, no. You can't change the apple ID email if you're using apple's email. I ran into this problem myself.

I signed up with a nickname email when I was younger. For example teenager@mac.com. You can later make an alias like John@mac.com. But every time you sign into iCloud, or write a new email on your phone, it's gonna default to teenager@mac.com.

It is a really bad issue for people that use apple's mac email exclusively.

And I can sympathize with the article. If you're divorced, and you change your name, you have to sign into iCloud with your ex husbands name every time you sign in or send a default email. You can't change it.

Once upon a time I had an apple ID, which I lost the password for. Many updates and machines later, it still lingers on somehow, and I cannot prevent that ID from showing up for updates and Mac App Store logins. It's a huge pain in the ass, just another drop in the "I hate Apple" bucket, and for that reason I sympathize with this rant.

NOTE: The ID shows up in the "ID" field next to password and I cannot change it by clicking. Why the hell would you design a UX like this Apple. Huge fail.