But there aren't dollars given to banks mostly. Cash is a tiny fraction of the money banks handle. Most of the payment volume is millions of electronics messages between banks to debit and credit numbers in people's accounts, and only at certain times of the day the net of that (a far, far smaller amount of reserves) are actually moved.
It's actually the other way around - trying to follow a physical dollar just makes you confused, because all the actual business of the bank is happening in accounting-land (the bank's balance sheets and electronic records of customer accounts).
You are splitting hairs where it doesn't matter. More alarmingly, by your reasoning the bank is not lending out cash either, so there is no value in considering 'cashflow' at all.
But in practice when people say they 'pay cash' for something large like a house or a car, they are usually effecting a bank transfer (well, in Korea at least). I understand that under the hood in the US this is an IOU between banks, but to the depositor there is no difference whether the money is cash or bits. What matters is whether the bank has the liquidity to provide upon request.
Then by your logic, shouldn’t banks not want customer deposits? Isn’t it just burdensome overhead?
Trust me, I get that people aren’t Fedexing cash envelopes between banks, but that doesn’t mean money is fake and banks can invent it out of think air (they can only multiply it)
And to be clear, again, you can very easily follow physical dollars at banks (otherwise imagine the fraud that could happen!), it’s just circular so multipliers get applied.
Like I get it’s complicated, but my deposit goes into a mortgage that then goes into another account, etc etc etc. that’s called the “credit multiplier” and we can definitely track it.
It's actually the other way around - trying to follow a physical dollar just makes you confused, because all the actual business of the bank is happening in accounting-land (the bank's balance sheets and electronic records of customer accounts).