My wife used to be a credit union teller. They physically did a count at the end of the day. All the bills had to be face up, no turned corners, etc. $2 bills just messed up the drawer counts. Dollar coins messed up the hand counts, too. Don’t know if her place ever went to machine counting as she moved onto a different job and it was many years ago. Financial processing and the like lean towards efficiencies. $2 bills and $1 coins are legal tender but mess up the counts. It’s the “price we pay” in a modern society.
I've noticed this over the last couple years , what happened to 'banknoting' , all the Bills facing the same way , face up. Even money I've received from banks are each other way. It used to be a standard. Easier to count. One way of telling if someone had a job handling cash was the money in their wallet was always 'banknoted' . I still do this.