You probably use direct deposit in which case your employer already has your banking info
In most cases, that's an external payroll service, not the actual employer that has that info.
People often have accounts at multiple banks…
your employer knows how much they paid you and what account they paid to. They don't know your balance, where else you might be getting money from (selling science fiction short stories eh, Cosgrove?! This job should be enough for you!!), that you have donated money to the Democrats recently!! We suggested that was bad!! And lots of other things that come under banking info.
They have my account and transit number and stuff, sure, that's different than my username and password for online banking. We print them out on cheques that can be (reasonably) safely given to my plumber.
patio11/bitsaboutmoney has some good writing about this