I have tried to remove my publicly visible email address several times from the SuperUser section. I have removed it and clicked Save, and Save for all StackOverflow sites.

Only the Super User website shows it under my profile, the other sites show it as empty.

I assume it's not visible based upon an answer I got at https://meta.stackexchange.com/questions/145863/possible-bug-in-user-profile-on-superuser-only#comment417231_145863 but they suggested I also informed you in case you want to action it.