As said previously, i am new and maybe i forgot to read something about bank system. in that case, erase my suggestion
But i have seen in this game is that many things are based on supply and demand. But not the bank system.
The bank system is only based on supply (loans) but not on the demand side (deposits). I won't run into the philosophical discussion about deposit making loans or loans making deposits in the monetary theory even though i like the debate, but ...
but i think that a newborn should be able to put his savings into a bank and getting a rate of interest in return (as in real life banks).
The higher the amount of capital we have, the lower the rate of interest will be (for deposits and for loans).
I think that the banks system should be a real one like the warehouse system. And this could be linked to the idea of building a real city in a port even with a Fort.
Banks should be linked to a port, so people will decide if bury their treasure or to deposit it in one bank in a specific port. Of course, the higher the capital in the specific port is, the lower the rate of interest will be (it's the same in real life, countries with macroeconomics risks or with low capitals will have higher rates of interest - ex. Greece - while "strong" countries and rich - ex. Germany - have low rates of interest).
But at the same time ports can be plundered and there is a chance to plunder a bank and all its deposits (or a part). So i think that in that case, managing a bank will be much more complicate, but even worthy for a guild or a nation to defend and focus on bank system as well focusing on military and trading side.
At the moment i see the bank system only as a way to hide billions of gold coins from being plundered. At the end nobody wants to be in debt at the start, so as a newcomer you wait that your guild will supply you with tons of free loans or free bank accounts. But the same system could be done by adding a rate of interests to deposits. It could be a way to attract deposits in some banks instead of others, or funds to banks related to a nation instead of one other.