If someone has your bank account and bank’s routing number (which is also not secret), they can make fraudulent ACH transfers and payments from your account. Of course it will most likely be caught as fraud some time after the fact, but just those two bits of not-secret info are enough to grief someone.

Knuth had to stop sending real checks for errors spotted in his books because they would post pics of the check and thieves abused the account https://www-cs-faculty.stanford.edu/~knuth/news08.html

And both numbers, plus your name and address and a convenient sample of your signature, are on every check you’ve ever written.