Take care of your stash!
The bank allows you to keep your cash safe.
Carrying too much money around with you often attracts unwanted attention. If another cash-strapped gangster notices you've got a decent amount of cash on your person, you could easily find yourself being shot at.
If you end up being killed, your murderer will take every dollar on your person, and he / she won't care how blood stained the dollar bills are!
By placing your cash in the bank nobody can see how much you are worth, and, should the worst happen, your friends will get a decent payout when your will is read out.