Generally, as you said, but if we as customers are still prioritized and if the supply runs out, they just take it back to their larger head office. There are also moments that create such conditions when many people need fiat in cash, for example during elections or other things, but personally I see that banks have anticipatory steps for important moments like this.
In essence, the mission of banks is to create slavery and poverty, they subtly colonize when we are free but suffer more. Indeed, they have provided sufficient security, of course we have to give them something in return. The way the bank receives this reward from us is by charging an administration fee that we have to pay every month, and the interest given by the bank also tends to be small. So when we save money in the bank, the rate of increase in value we have is slow and the money we have does not increase. Not to mention what you said, when making large withdrawals takes a long time, it is prioritized as you said, but to make it a priority we have to report it first to the bank, right? Doesn't this make things difficult? So if you think about it again, there is no significant benefit from saving at the bank. It is better to invest in bitcoin which clearly has freedom and can create healthy finances in the future.