FRB isn't how banking has ever worked, even when we used commodity money, but it's a relatively simple concept that matches peoples' intuitive sense of money as a fixed amount of tokens used to store wealth. But money's purpose is to facilitate transactions and be a unit of account which should be thought of through the lens of double-entry accounting, something almost nobody does.
Banks would always have tracked accounts via ledgers though, it's just that before fiat currencies they had reserve requirements in place to ensure banks kept enough currency on hand to handle day to day withdrawals.
> This is not how money is actually created but only a way to represent the possible impact of the fractional reserve system on the money supply. As such, while is useful for economics professors, it is generally regarded as an oversimplification by policymakers.
And from the Bank of England's (very good) primer on money creation:
> Money creation in practice differs from some popular misconceptions — banks do not act simply as intermediaries, lending out deposits that savers place with them, and nor do they ‘multiply up’ central bank money to create new loans and deposits.
> ...
> Rather than banks receiving deposits when households save and then lending them out, bank lending creates deposits
The "money multiplier" concept of FRB is a useful model in the same sense that modelling an atom as if it were like a solar system with a solid nucleus with electrons whizzing around it like planets i.e. not really 'true' but a useful-enough approximation for many use cases.
The BoE primer explains all of this very clearly on the first couple of pages, it's well worth reading:
Banks would always have tracked accounts via ledgers though, it's just that before fiat currencies they had reserve requirements in place to ensure banks kept enough currency on hand to handle day to day withdrawals.