Are users not able to remove their email because no one has cared to implement it yet? or is there a deeper reason for this?

Looks like if you leave a blank "New email address" field in Special:ChangeEmail, you can remove your email address.. This definitely needs to be made more obvious.

Change 241686 had a related patch set uploaded (by Glaisher):
Make it more obvious that users can remove their email address

https://gerrit.wikimedia.org/r/241686

Change 241709 had a related patch set uploaded (by BryanDavis):
Give instructions on removing email address from account

https://gerrit.wikimedia.org/r/241709

Does a change to NO email address still need to be confirmed by the user at the original address?

If we are going to make the removal of an email address more visible/obvious, then we also need to make evident the consequences of such an action, ie.

By removing this email address you will no longer be able to retrieve or reset a lost password.
Such accounts will not be able to be resurrected or reallocated should you lose your password.

Internal note that this presumably makes it easier to vandalise an account, in that if someone gets into the account then changes it to nothing that there is less ability to identify its previous target?

Change 241709 merged by jenkins-bot:
Give instructions on removing email address from account

https://gerrit.wikimedia.org/r/241709

@Billinghurst: If the mail address is not removed, but changed to something different, is the original recipient notified about that? Otherwise you would have the same threat there.

yes @scfc, with a change of email address, there is the requirement to confirm the new email address from the originating email address

A note about the consequences of removing the email address will also be shown to the user.

Change 241686 merged by jenkins-bot:
Make it more obvious that users can remove their email address

https://gerrit.wikimedia.org/r/241686