It's relatively common for it to be a privacy concern. Imagine if I'm making an online payment or something, and one of the IDs involved tells you exactly when I created my bank account. That's a decent proxy for my age.
Knowing approximate age is a relatively small leak compared to that.
Bank security does not depend on your bank account being private information. Pretty much all bank security rounds to the bank having a magic undo button, so they can undo any bad transactions after it comes to light that it was a bad transaction. Sure they do some filtering on the front-end now to eliminate the need to use the magic undo button, but that's just extra icing to keep the undo button's use to a dull roar.