Hi Dave,
Emma did a good job covering most of this, but I just wanted to add that one of the reasons we do not send a confirmation/permission email to the old address, is that a couple of valid reasons for changing your email in Moodle could be that the old address was compromised, or that you have otherwise lost access to it. In your example, it's possible you could have forgotten to update it prior to your job change, in which case you would have lost access to the email account and would have no way to verify the email address change.
Emma did a good job covering most of this, but I just wanted to add that one of the reasons we do not send a confirmation/permission email to the old address, is that a couple of valid reasons for changing your email in Moodle could be that the old address was compromised, or that you have otherwise lost access to it. In your example, it's possible you could have forgotten to update it prior to your job change, in which case you would have lost access to the email account and would have no way to verify the email address change.
Although you do need to be logged in to change the email address, we do also have a "best practice" improvement in our backlog to require re-authentication when changing sensitive user details, such as email (see MDL-70177 for further information).