It seems that I'm unable to persistently remove my email address from my profile pages.

Initially removing my email address works fine, I simply visit my profile page on any site associated with my account, edit my email and press the `Save And Copy Profile To All Stack Exchange Accounts` button. So far, so good.

However, if I'm logged out; whether logging out manually or visiting the site from a new device; I then log into any of my sites using the Stack Exchange method and the following happens:

 - For the profile page on that site, the email field is automatically re-populated. 
 - For the profile page on subsequently visited sites, I'm automatically logged in but the email field remains empty.
 - I have tested logging into each of the sites and it's only ever the first site that I log into where the profile pages get repopulated with my email address.

Is this expected behavior of Stack Exchange sites or a bug?

Other things to note:

 - I assume that the email address field on the profile pages are not mandatory.
 - The email address that is repopulated is one I use to log in with the Stack Exchange method.
 - My motives in trying isn't out of email privacy but simply bafflement. I'm aware that [your profile email address is only visible to yourself and moderators][1].

  [1]: http://meta.stackexchange.com/questions/77453/how-to-make-e-mail-invisible-on-stack-exchange-profile/77454#77454