Yes, it sounds very simple. But I think it might work, maybe with a little tweaking.
What you do is, you appoint a banker noble. He needs, or will acquire, the record keeper and appraiser skills. (Maybe organizer too?) Banking is all he does.
He will work in the "bank" building, which can be made out of a chair (for him to sit at), a table, and a bin (to keep coins in).
Metalcrafters will still mint coins. But what about coin stockpiles? Ah, there's the beauty of it! The bank *is* the coin stockpile. Dwarves will receive coins from their bosses (probably not gonna be implemented for some time) or from being paid for things, and they will not haul their coins to the bank until they go on break.
The other beauty of this is, banks have never really moved money around. They simply shift numbers on ledgers. This means that if you do not appoint a banker noble, dwarves are going to keep using a "broken" economy- they'll keep splitting coins up and create so many hauling jobs that nothing gets done. But, when you appoint a banker noble, they only have to pay for a few things, like trinkets and (maybe?) food or drink, and we could probably have them carry some coins on their possession like they might wear a silk sock. For things like rent, why have the dwarves themselves pay? The banker can just subtract some cash from their account. Wages can work the same way. Food and drink could work as a bill that gets subtracted at the end of the month.