1920s thinking? What money in the vault?
More like 3rd world country. There are still a not so many, yet not so few money in our bank's vaults. That's why big withdrawals need to be informed beforehand.
When a company deposits a paycheck for an employee, does someone run down to the bank with cash?
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.
Banks dont want cash. It is dirty, they have to store it, and a pain in the ass to move around.
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.