Well I've been toying with this thought for some time now, and I can not come up with an answer. However, I have 2 suggestions to bounce off of you to see if we can add to make more sense out of them.

Bank Robbery. Similar to how organized crimes are run, you and a group of mobsters can rob the city bank of one of the 8 cities. When you rob said bank, the money that is forcefully removed will be distributed equally amongst the people with a positive balance in that cities bank. Obviously people who have large sums of money in their account would only see a percentage of it in loss, whereas, someone who had a small amount may see the account completely wiped out.

Or

Bank Fees. Having an account in a city that is not of your home city you need someone to protect it. Who could fill these shoes? Well that cities godfather of course. For a nominal weekly fee of a percentage of what is in the account which ever is greater would be automatically deducted and paid out to that cities godfather.
But Howard, if we know that the money is going to be taken out each week on say Monday morning at midnight wouldn't we just make a withdraw our money from the account.
Sure, but what if the godfather had to collect his fees. So the godfather went to the local bank sometime between midnight and noon on Monday to collect the weekly bank fees.
What if the godfather forgets?
well, then (s)he is out of luck. If you don't go to rob the post office, they wont just hand you the money. Therefore if the godfather doesn't collect his fees in a timely manner they will not be paid out.

i can't say i like the bank fees, but i do like the bank robbery idea.

as to your question, the city banks are mainly for tributes that come in to sponsor and crew leaders. by using the city banks for tributes, it force crew leaders and sponsor to actively collec the tribute their associates bring in.

I like the bank robbery. Its kinda like a Organised PP. Get a few people together to take money off someone. Sounds fun.

Also good for gambling addicts, I've always assumed.

Vasily, I can definitely support your response. :)