Reading further the Fiat Standard book by Saifedean Ammous, one of the eye-opening things is about the distinction between monetary and payment systems – and its exactly not understanding these things why people wrongfully compare Bitcoin to VISA and conclude that Bitcoin is slow, thus it can't have any impactful role in a global scale.
In the gold standard the monetary system was based on gold. When gold coins were used, they were analogous to final settlements. The trading of notes – paper claims with x amount value in gold – was a payment system in the gold standard and also a means of scaling.
In today's fiat standard, the monetary system is based on the rules of government with central banks in charge of the money supply. VISA is a digital payment system in the fiat standard. When VISA processes a payment, no actual fiat money is moved, the actual money moves later in a final settlement where the payments are added together.
Bitcoin as a final settlement layer
The important thing to understand that in a global Bitcoin Standard, bitcoin network functions as a final settlement layer which means that it's not even supposed to record every single payment that happens, because if it could, the blockchain size would be so bloated that it would be impossible for any regular person to run a node. Nodes ensure the integrity and decentralization of the bitcoin network and if they would get expensive to run, it would centralize nodes and expose the network for exploitation.
Similarly to other systems, scaling solutions – like Lightning Network – will process most of the payments. Then bigger institutions and banks will use the base layer for final settlements. Yes, banking could and probably will exist in a Bitcoin standard, but the key difference to today's banking is that commercial banks will provide a service, whereas now they are involved with processing payments and increasing money supply by creating debt.
In a Bitcoin standard banks would only process payments and not be involved in money creation. In a Bitcoin standard if a bank gives out "bitcoin claims" more than what Bitcoin they hold in reserve, this can be seen because Bitcoin is a public ledger, thus such banks would run out of business, because people wouldn't deposit their money in such a bank.
Bitcoin would hold banks and institutions accountable similarly how you and me as regular people need to balance our incomes and outcomes. In a bitcoin standard banks can't create money out of thin air with debt to finance their unproductive spending and export the cost of it to the holders of the money via inflation.
So by holding Bitcoin, you actually have stake in a future settlement layer of a global monetary system that can't be inflated by any entity for their own benefit, should that happen. By holding fiat money in a bank account, you hold monetized debt. Central banks hold the base layer money, and you (most likely) don't have access to that.