I never understood why I need a transaction number for every wire transfer I do (this is Germany) which is sent directly by the bank via mail with no mention of

I never understood why I need a transaction number for every wire transfer I do (this is Germany) which is sent directly by the bank via mail with no mention of the associated bank account. Account numbers are public and printed on every letter head, but the TANs are the key to withdraw money from it online. Been using it for 17 years, never had a problem. But I cursed the system a lot since it's such a hassle. Some banks even send you a piece of hardware you have to put against the screen (!) with a bar code to show you the next TAN. It's ridiculous.