Banks dont want cash. It is dirty, they have to store it, and a pain in the ass to move around.
I've actually seen this happen loads of times, especially with small companies. They send their messengers to do it, and I see them with wads of cash depositing to the teller.
If they are in a cash business like restaurants, sure. However, they are running to employees banks with cash to had the teller and saying deposit this in Joe Smiths account, it is his paycheck.