Depending on how and how fast things happen, your data may have already gone by the time you got the notification
Totally agree with that, but still better than having nothing 😉
Not everyone uses a valid (in terms of being active) so many of the users won't receive the notification message
It only would be a real security improvement if tho old mail gets the verification. If someone used a trash mail to register this service (which is btw pretty stupid, 'cause you save important data here) then this is just bad luck for him/her. An early announcement can be helpful at this point.