[Brian_K_White]

It is not sufficient.

The amount of disclosed information, and it's utility, is non-zero, but simply weighs less than the amount of damage from not hinting which account to check.

Accounts can grow to be 20 years old and even a "normal" person who is not actively using lots of addresses for security, will still end up having used several in the fullness of time and completely forgotten about some, yet, may still have or can regain access to them if only they knew to go look.

You don't see how that can happen or really be a problem? Oh well, consider yourself informed that it does happen and is a problem.